LMFDB - Embedded newform 798.2.p.c.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(107,798)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("798.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	798.107
Dual form			798.2.p.c.179.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.69615 + 0.350829i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(1.69615 - 0.350829i) q^{6} +(-1.01122 - 2.44488i) q^{7} -1.00000 q^{8} +(2.75384 - 1.19012i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.69615 + 0.350829i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(1.69615 - 0.350829i) q^{6} +(-1.01122 - 2.44488i) q^{7} -1.00000 q^{8} +(2.75384 - 1.19012i) q^{9} -4.07740i q^{10} +(-0.930342 + 0.537133i) q^{11} +(-1.69615 + 0.350829i) q^{12} +(5.50387 + 3.17766i) q^{13} +(1.01122 + 2.44488i) q^{14} +(-1.43047 - 6.91588i) q^{15} +1.00000 q^{16} +(2.61890 + 1.51203i) q^{17} +(-2.75384 + 1.19012i) q^{18} +(4.34265 + 0.375980i) q^{19} +4.07740i q^{20} +(2.57291 + 3.79211i) q^{21} +(0.930342 - 0.537133i) q^{22} +(5.87482 - 3.39183i) q^{23} +(1.69615 - 0.350829i) q^{24} -11.6252 q^{25} +(-5.50387 - 3.17766i) q^{26} +(-4.25339 + 2.98474i) q^{27} +(-1.01122 - 2.44488i) q^{28} +(-2.84891 + 4.93446i) q^{29} +(1.43047 + 6.91588i) q^{30} +(-4.45649 + 2.57296i) q^{31} -1.00000 q^{32} +(1.38956 - 1.23745i) q^{33} +(-2.61890 - 1.51203i) q^{34} +(9.96876 - 4.12315i) q^{35} +(2.75384 - 1.19012i) q^{36} +(3.66771 + 2.11756i) q^{37} +(-4.34265 - 0.375980i) q^{38} +(-10.4502 - 3.45886i) q^{39} -4.07740i q^{40} +(-1.99215 - 3.45051i) q^{41} +(-2.57291 - 3.79211i) q^{42} +(-3.14519 - 5.44764i) q^{43} +(-0.930342 + 0.537133i) q^{44} +(4.85258 + 11.2285i) q^{45} +(-5.87482 + 3.39183i) q^{46} +(-3.44099 + 1.98666i) q^{47} +(-1.69615 + 0.350829i) q^{48} +(-4.95487 + 4.94462i) q^{49} +11.6252 q^{50} +(-4.97251 - 1.64583i) q^{51} +(5.50387 + 3.17766i) q^{52} -4.73673 q^{53} +(4.25339 - 2.98474i) q^{54} +(-2.19011 - 3.79338i) q^{55} +(1.01122 + 2.44488i) q^{56} +(-7.49769 + 0.885812i) q^{57} +(2.84891 - 4.93446i) q^{58} +(-4.16467 + 7.21341i) q^{59} +(-1.43047 - 6.91588i) q^{60} +(3.84448 + 6.65884i) q^{61} +(4.45649 - 2.57296i) q^{62} +(-5.69443 - 5.52933i) q^{63} +1.00000 q^{64} +(-12.9566 + 22.4415i) q^{65} +(-1.38956 + 1.23745i) q^{66} +7.59056i q^{67} +(2.61890 + 1.51203i) q^{68} +(-8.77462 + 7.81411i) q^{69} +(-9.96876 + 4.12315i) q^{70} +(4.36350 + 7.55780i) q^{71} +(-2.75384 + 1.19012i) q^{72} +(4.19824 - 7.27157i) q^{73} +(-3.66771 - 2.11756i) q^{74} +(19.7181 - 4.07846i) q^{75} +(4.34265 + 0.375980i) q^{76} +(2.25401 + 1.73141i) q^{77} +(10.4502 + 3.45886i) q^{78} +6.87993i q^{79} +4.07740i q^{80} +(6.16725 - 6.55477i) q^{81} +(1.99215 + 3.45051i) q^{82} -0.0397535i q^{83} +(2.57291 + 3.79211i) q^{84} +(-6.16514 + 10.6783i) q^{85} +(3.14519 + 5.44764i) q^{86} +(3.10102 - 9.36905i) q^{87} +(0.930342 - 0.537133i) q^{88} +(0.110424 + 0.191260i) q^{89} +(-4.85258 - 11.2285i) q^{90} +(2.20337 - 16.6696i) q^{91} +(5.87482 - 3.39183i) q^{92} +(6.65621 - 5.92759i) q^{93} +(3.44099 - 1.98666i) q^{94} +(-1.53302 + 17.7067i) q^{95} +(1.69615 - 0.350829i) q^{96} +(12.0392 - 6.95084i) q^{97} +(4.95487 - 4.94462i) q^{98} +(-1.92276 + 2.58639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 50 q^{2} - 3 q^{3} + 50 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9}+O(q^{10}) $ 50 * q - 50 * q^2 - 3 * q^3 + 50 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9	$ 50 q - 50 q^{2} - 3 q^{3} + 50 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 17 q^{15} + 50 q^{16} - 3 q^{17} + 3 q^{18} + 10 q^{19} + 4 q^{21} - 3 q^{22} - 9 q^{23} + 3 q^{24} - 58 q^{25} + 3 q^{26} - 6 q^{27} + 5 q^{29} + 17 q^{30} + 15 q^{31} - 50 q^{32} + q^{33} + 3 q^{34} - 3 q^{36} - 9 q^{37} - 10 q^{38} - 17 q^{39} + 17 q^{41} - 4 q^{42} + 15 q^{43} + 3 q^{44} + 26 q^{45} + 9 q^{46} - 21 q^{47} - 3 q^{48} + 8 q^{49} + 58 q^{50} - 23 q^{51} - 3 q^{52} + 12 q^{53} + 6 q^{54} - 16 q^{55} - 4 q^{57} - 5 q^{58} + q^{59} - 17 q^{60} + 23 q^{61} - 15 q^{62} - 16 q^{63} + 50 q^{64} + 14 q^{65} - q^{66} - 3 q^{68} + 31 q^{69} - 3 q^{71} + 3 q^{72} + 15 q^{73} + 9 q^{74} + 8 q^{75} + 10 q^{76} + 57 q^{77} + 17 q^{78} + 77 q^{81} - 17 q^{82} + 4 q^{84} - 10 q^{85} - 15 q^{86} + 19 q^{87} - 3 q^{88} - 33 q^{89} - 26 q^{90} - 15 q^{91} - 9 q^{92} + 53 q^{93} + 21 q^{94} - 30 q^{95} + 3 q^{96} - 21 q^{97} - 8 q^{98} + 19 q^{99}+O(q^{100}) $ 50 * q - 50 * q^2 - 3 * q^3 + 50 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 17 * q^15 + 50 * q^16 - 3 * q^17 + 3 * q^18 + 10 * q^19 + 4 * q^21 - 3 * q^22 - 9 * q^23 + 3 * q^24 - 58 * q^25 + 3 * q^26 - 6 * q^27 + 5 * q^29 + 17 * q^30 + 15 * q^31 - 50 * q^32 + q^33 + 3 * q^34 - 3 * q^36 - 9 * q^37 - 10 * q^38 - 17 * q^39 + 17 * q^41 - 4 * q^42 + 15 * q^43 + 3 * q^44 + 26 * q^45 + 9 * q^46 - 21 * q^47 - 3 * q^48 + 8 * q^49 + 58 * q^50 - 23 * q^51 - 3 * q^52 + 12 * q^53 + 6 * q^54 - 16 * q^55 - 4 * q^57 - 5 * q^58 + q^59 - 17 * q^60 + 23 * q^61 - 15 * q^62 - 16 * q^63 + 50 * q^64 + 14 * q^65 - q^66 - 3 * q^68 + 31 * q^69 - 3 * q^71 + 3 * q^72 + 15 * q^73 + 9 * q^74 + 8 * q^75 + 10 * q^76 + 57 * q^77 + 17 * q^78 + 77 * q^81 - 17 * q^82 + 4 * q^84 - 10 * q^85 - 15 * q^86 + 19 * q^87 - 3 * q^88 - 33 * q^89 - 26 * q^90 - 15 * q^91 - 9 * q^92 + 53 * q^93 + 21 * q^94 - 30 * q^95 + 3 * q^96 - 21 * q^97 - 8 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.69615	+	0.350829i	−0.979272	+	0.202551i
$3$	−1.69615	+	0.350829i	−0.979272	+	0.202551i
$4$	1.00000			0.500000
$5$			4.07740i			1.82347i	0.410779	+	0.911735i	$0.365257\pi$
$5$			4.07740i			1.82347i	−0.410779	+	0.911735i	$0.634743\pi$
$6$	1.69615	−	0.350829i	0.692450	−	0.143225i
$7$	−1.01122	−	2.44488i	−0.382205	−	0.924077i
$7$	−1.01122	−	2.44488i	−0.382205	−	0.924077i
$8$	−1.00000			−0.353553
$9$	2.75384	−	1.19012i	0.917946	−	0.396705i
$10$		−	4.07740i		−	1.28939i
$11$	−0.930342	+	0.537133i	−0.280509	+	0.161952i	−0.633654	−	0.773617i	$-0.718446\pi$
$11$	−0.930342	+	0.537133i	−0.280509	+	0.161952i	0.353145	+	0.935569i	$0.385112\pi$
$12$	−1.69615	+	0.350829i	−0.489636	+	0.101276i
$13$	5.50387	+	3.17766i	1.52650	+	0.881324i	0.999505	+	0.0314543i	$0.0100139\pi$
$13$	5.50387	+	3.17766i	1.52650	+	0.881324i	0.526993	+	0.849870i	$0.323319\pi$
$14$	1.01122	+	2.44488i	0.270260	+	0.653421i
$15$	−1.43047	−	6.91588i	−0.369346	−	1.78567i
$16$	1.00000			0.250000
$17$	2.61890	+	1.51203i	0.635178	+	0.366720i	0.782755	−	0.622331i	$-0.213814\pi$
$17$	2.61890	+	1.51203i	0.635178	+	0.366720i	−0.147577	+	0.989051i	$0.547147\pi$
$18$	−2.75384	+	1.19012i	−0.649086	+	0.280513i
$19$	4.34265	+	0.375980i	0.996273	+	0.0862557i
$19$	4.34265	+	0.375980i	0.996273	+	0.0862557i
$20$			4.07740i			0.911735i
$21$	2.57291	+	3.79211i	0.561456	+	0.827507i
$22$	0.930342	−	0.537133i	0.198350	−	0.114517i
$23$	5.87482	−	3.39183i	1.22499	−	0.707246i	0.259009	−	0.965875i	$-0.416604\pi$
$23$	5.87482	−	3.39183i	1.22499	−	0.707246i	0.965977	+	0.258629i	$0.0832708\pi$
$24$	1.69615	−	0.350829i	0.346225	−	0.0716127i
$25$	−11.6252			−2.32504
$26$	−5.50387	−	3.17766i	−1.07940	−	0.623190i
$27$	−4.25339	+	2.98474i	−0.818565	+	0.574413i
$28$	−1.01122	−	2.44488i	−0.191103	−	0.462039i
$29$	−2.84891	+	4.93446i	−0.529029	+	0.916306i	0.470397	+	0.882455i	$0.344111\pi$
$29$	−2.84891	+	4.93446i	−0.529029	+	0.916306i	−0.999427	+	0.0338512i	$0.989223\pi$
$30$	1.43047	+	6.91588i	0.261167	+	1.26266i
$31$	−4.45649	+	2.57296i	−0.800410	+	0.462117i	−0.843615	−	0.536949i	$-0.819577\pi$
$31$	−4.45649	+	2.57296i	−0.800410	+	0.462117i	0.0432045	+	0.999066i	$0.486243\pi$
$32$	−1.00000			−0.176777
$33$	1.38956	−	1.23745i	0.241891	−	0.215412i
$34$	−2.61890	−	1.51203i	−0.449138	−	0.259310i
$35$	9.96876	−	4.12315i	1.68503	−	0.696940i
$36$	2.75384	−	1.19012i	0.458973	−	0.198353i
$37$	3.66771	+	2.11756i	0.602968	+	0.348124i	0.770208	−	0.637792i	$-0.220152\pi$
$37$	3.66771	+	2.11756i	0.602968	+	0.348124i	−0.167240	+	0.985916i	$0.553486\pi$
$38$	−4.34265	−	0.375980i	−0.704471	−	0.0609920i
$39$	−10.4502	−	3.45886i	−1.67337	−	0.553862i
$40$		−	4.07740i		−	0.644694i
$41$	−1.99215	−	3.45051i	−0.311122	−	0.538880i	0.667483	−	0.744625i	$-0.267372\pi$
$41$	−1.99215	−	3.45051i	−0.311122	−	0.538880i	−0.978606	+	0.205745i	$0.934038\pi$
$42$	−2.57291	−	3.79211i	−0.397009	−	0.585136i
$43$	−3.14519	−	5.44764i	−0.479638	−	0.830757i	0.520090	−	0.854112i	$-0.325899\pi$
$43$	−3.14519	−	5.44764i	−0.479638	−	0.830757i	−0.999727	+	0.0233549i	$0.992565\pi$
$44$	−0.930342	+	0.537133i	−0.140254	+	0.0809759i
$45$	4.85258	+	11.2285i	0.723380	+	1.67385i
$46$	−5.87482	+	3.39183i	−0.866196	+	0.500098i
$47$	−3.44099	+	1.98666i	−0.501920	+	0.289784i	−0.729506	−	0.683974i	$-0.760250\pi$
$47$	−3.44099	+	1.98666i	−0.501920	+	0.289784i	0.227586	+	0.973758i	$0.426917\pi$
$48$	−1.69615	+	0.350829i	−0.244818	+	0.0506378i
$49$	−4.95487	+	4.94462i	−0.707838	+	0.706375i
$50$	11.6252			1.64405
$51$	−4.97251	−	1.64583i	−0.696291	−	0.230462i
$52$	5.50387	+	3.17766i	0.763249	+	0.440662i
$53$	−4.73673			−0.650640			−0.325320	−	0.945604i	$-0.605472\pi$
$53$	−4.73673			−0.650640			−0.325320	+	0.945604i	$0.605472\pi$
$54$	4.25339	−	2.98474i	0.578813	−	0.406172i
$55$	−2.19011	−	3.79338i	−0.295314	−	0.511499i
$56$	1.01122	+	2.44488i	0.135130	+	0.326711i
$57$	−7.49769	+	0.885812i	−0.993093	+	0.117329i
$58$	2.84891	−	4.93446i	0.374080	−	0.647926i
$59$	−4.16467	+	7.21341i	−0.542193	+	0.939106i	0.456584	+	0.889680i	$0.349073\pi$
$59$	−4.16467	+	7.21341i	−0.542193	+	0.939106i	−0.998778	+	0.0494264i	$0.984261\pi$
$60$	−1.43047	−	6.91588i	−0.184673	−	0.892836i
$61$	3.84448	+	6.65884i	0.492236	+	0.852577i	0.999960	−	0.00894224i	$-0.00284644\pi$
$61$	3.84448	+	6.65884i	0.492236	+	0.852577i	−0.507724	+	0.861520i	$0.669513\pi$
$62$	4.45649	−	2.57296i	0.565975	−	0.326766i
$63$	−5.69443	−	5.52933i	−0.717430	−	0.696630i
$64$	1.00000			0.125000
$65$	−12.9566	+	22.4415i	−1.60707	+	2.78352i
$66$	−1.38956	+	1.23745i	−0.171043	+	0.152319i
$67$			7.59056i			0.927334i	0.886010	+	0.463667i	$0.153467\pi$
$67$			7.59056i			0.927334i	−0.886010	+	0.463667i	$0.846533\pi$
$68$	2.61890	+	1.51203i	0.317589	+	0.183360i
$69$	−8.77462	+	7.81411i	−1.05634	+	0.940708i
$70$	−9.96876	+	4.12315i	−1.19149	+	0.492811i
$71$	4.36350	+	7.55780i	0.517852	+	0.896946i	0.999785	+	0.0207377i	$0.00660149\pi$
$71$	4.36350	+	7.55780i	0.517852	+	0.896946i	−0.481933	+	0.876208i	$0.660065\pi$
$72$	−2.75384	+	1.19012i	−0.324543	+	0.140257i
$73$	4.19824	−	7.27157i	0.491367	−	0.851073i	−0.508584	−	0.861013i	$-0.669831\pi$
$73$	4.19824	−	7.27157i	0.491367	−	0.851073i	0.999951	+	0.00993997i	$0.00316404\pi$
$74$	−3.66771	−	2.11756i	−0.426363	−	0.246161i
$75$	19.7181	−	4.07846i	2.27685	−	0.470940i
$76$	4.34265	+	0.375980i	0.498137	+	0.0431278i
$77$	2.25401	+	1.73141i	0.256868	+	0.197313i
$78$	10.4502	+	3.45886i	1.18325	+	0.391639i
$79$			6.87993i			0.774052i	0.922069	+	0.387026i	$0.126498\pi$
$79$			6.87993i			0.774052i	−0.922069	+	0.387026i	$0.873502\pi$
$80$			4.07740i			0.455867i
$81$	6.16725	−	6.55477i	0.685250	−	0.728308i
$82$	1.99215	+	3.45051i	0.219997	+	0.381045i
$83$		−	0.0397535i		−	0.00436352i	−0.999998	−	0.00218176i	$-0.999306\pi$
$83$		−	0.0397535i		−	0.00436352i	0.999998	−	0.00218176i	$-0.000694476\pi$
$84$	2.57291	+	3.79211i	0.280728	+	0.413753i
$85$	−6.16514	+	10.6783i	−0.668703	+	1.15823i
$86$	3.14519	+	5.44764i	0.339155	+	0.587434i
$87$	3.10102	−	9.36905i	0.332465	−	1.00447i
$88$	0.930342	−	0.537133i	0.0991748	−	0.0572586i
$89$	0.110424	+	0.191260i	0.0117049	+	0.0202735i	0.871819	−	0.489829i	$-0.162941\pi$
$89$	0.110424	+	0.191260i	0.0117049	+	0.0202735i	−0.860114	+	0.510102i	$0.829607\pi$
$90$	−4.85258	−	11.2285i	−0.511507	−	1.18359i
$91$	2.20337	−	16.6696i	0.230976	−	1.74745i
$92$	5.87482	−	3.39183i	0.612493	−	0.353623i
$93$	6.65621	−	5.92759i	0.690217	−	0.614662i
$94$	3.44099	−	1.98666i	0.354911	−	0.204908i
$95$	−1.53302	+	17.7067i	−0.157285	+	1.81667i
$96$	1.69615	−	0.350829i	0.173112	−	0.0358063i
$97$	12.0392	−	6.95084i	1.22240	−	0.705751i	0.256968	−	0.966420i	$-0.417276\pi$
$97$	12.0392	−	6.95084i	1.22240	−	0.705751i	0.965428	+	0.260669i	$0.0839430\pi$
$98$	4.95487	−	4.94462i	0.500517	−	0.499482i
$99$	−1.92276	+	2.58639i	−0.193245	+	0.259942i
$100$	−11.6252			−1.16252
$101$			8.79633i			0.875267i	0.899153	+	0.437634i	$0.144183\pi$
$101$			8.79633i			0.875267i	−0.899153	+	0.437634i	$0.855817\pi$
$102$	4.97251	+	1.64583i	0.492352	+	0.162962i
$103$	−11.3862	−	6.57382i	−1.12192	−	0.647738i	−0.180026	−	0.983662i	$-0.557618\pi$
$103$	−11.3862	−	6.57382i	−1.12192	−	0.647738i	−0.941889	+	0.335924i	$0.890952\pi$
$104$	−5.50387	−	3.17766i	−0.539699	−	0.311595i
$105$	−15.4620	+	10.4908i	−1.50893	+	1.02380i
$106$	4.73673			0.460072
$107$	−1.67647	+	2.90374i	−0.162071	+	0.280715i	−0.935611	−	0.353032i	$-0.885151\pi$
$107$	−1.67647	+	2.90374i	−0.162071	+	0.280715i	0.773540	+	0.633747i	$0.218484\pi$
$108$	−4.25339	+	2.98474i	−0.409283	+	0.287207i
$109$	−8.50939	−	4.91290i	−0.815052	−	0.470570i	0.0336554	−	0.999433i	$-0.489285\pi$
$109$	−8.50939	−	4.91290i	−0.815052	−	0.470570i	−0.848707	+	0.528863i	$0.822618\pi$
$110$	2.19011	+	3.79338i	0.208819	+	0.361685i
$111$	−6.96389	−	2.30495i	−0.660983	−	0.218776i
$112$	−1.01122	−	2.44488i	−0.0955513	−	0.231019i
$113$	−11.3167			−1.06458			−0.532292	−	0.846561i	$-0.678669\pi$
$113$	−11.3167			−1.06458			−0.532292	+	0.846561i	$0.678669\pi$
$114$	7.49769	−	0.885812i	0.702223	−	0.0829639i
$115$	13.8299	+	23.9540i	1.28964	+	2.23372i
$116$	−2.84891	+	4.93446i	−0.264515	+	0.458153i
$117$	18.9385	+	2.20052i	1.75087	+	0.203438i
$118$	4.16467	−	7.21341i	0.383389	−	0.664049i
$119$	1.04843	−	7.93190i	0.0961094	−	0.727116i
$120$	1.43047	+	6.91588i	0.130584	+	0.631331i
$121$	−4.92298	+	8.52684i	−0.447543	+	0.775168i
$122$	−3.84448	−	6.65884i	−0.348063	−	0.602863i
$123$	4.58953	+	5.15368i	0.413824	+	0.464691i
$124$	−4.45649	+	2.57296i	−0.400205	+	0.231058i
$125$		−	27.0137i		−	2.41617i
$126$	5.69443	+	5.52933i	0.507300	+	0.492592i
$127$	10.5158	+	6.07128i	0.933123	+	0.538739i	0.887798	−	0.460233i	$-0.152234\pi$
$127$	10.5158	+	6.07128i	0.933123	+	0.538739i	0.0453251	+	0.998972i	$0.485568\pi$
$128$	−1.00000			−0.0883883
$129$	7.24591	+	8.13657i	0.637966	+	0.716385i
$130$	12.9566	−	22.4415i	1.13637	−	1.96825i
$131$			12.7980i			1.11817i	0.829111	+	0.559084i	$0.188847\pi$
$131$			12.7980i			1.11817i	−0.829111	+	0.559084i	$0.811153\pi$
$132$	1.38956	−	1.23745i	0.120945	−	0.107706i
$133$	−3.47215	−	10.9975i	−0.301074	−	0.953601i
$134$		−	7.59056i		−	0.655724i
$135$	−12.1700	−	17.3428i	−1.04743	−	1.49263i
$136$	−2.61890	−	1.51203i	−0.224569	−	0.129655i
$137$		−	17.3126i		−	1.47911i	−0.673095	−	0.739556i	$-0.735035\pi$
$137$		−	17.3126i		−	1.47911i	0.673095	−	0.739556i	$-0.264965\pi$
$138$	8.77462	−	7.81411i	0.746945	−	0.665181i
$139$	0.616575	−	1.06794i	0.0522972	−	0.0905815i	−0.838692	−	0.544607i	$-0.816679\pi$
$139$	0.616575	−	1.06794i	0.0522972	−	0.0905815i	0.890989	+	0.454025i	$0.150012\pi$
$140$	9.96876	−	4.12315i	0.842514	−	0.348470i
$141$	5.13945	−	4.57686i	0.432820	−	0.385441i
$142$	−4.36350	−	7.55780i	−0.366177	−	0.634236i
$143$	−6.82731			−0.570928
$144$	2.75384	−	1.19012i	0.229486	−	0.0991764i
$145$	−20.1198	−	11.6162i	−1.67086	−	0.964669i
$146$	−4.19824	+	7.27157i	−0.347449	+	0.601799i
$147$	6.66947	−	10.1251i	0.550089	−	0.835106i
$148$	3.66771	+	2.11756i	0.301484	+	0.174062i
$149$		−	17.8685i		−	1.46385i	−0.681387	−	0.731923i	$-0.738623\pi$
$149$		−	17.8685i		−	1.46385i	0.681387	−	0.731923i	$-0.261377\pi$
$150$	−19.7181	+	4.07846i	−1.60997	+	0.333005i
$151$	−17.6780	+	10.2064i	−1.43862	+	0.830586i	−0.997754	−	0.0669889i	$-0.978661\pi$
$151$	−17.6780	+	10.2064i	−1.43862	+	0.830586i	−0.440863	+	0.897575i	$0.645327\pi$
$152$	−4.34265	−	0.375980i	−0.352236	−	0.0304960i
$153$	9.01153	+	1.04707i	0.728539	+	0.0846507i
$154$	−2.25401	−	1.73141i	−0.181633	−	0.139521i
$155$	−10.4910	−	18.1709i	−0.842656	−	1.45952i
$156$	−10.4502	−	3.45886i	−0.836685	−	0.276931i
$157$	7.34628	−	12.7241i	0.586297	−	1.01550i	−0.408415	−	0.912796i	$-0.633918\pi$
$157$	7.34628	−	12.7241i	0.586297	−	1.01550i	0.994712	−	0.102700i	$-0.0327482\pi$
$158$		−	6.87993i		−	0.547338i
$159$	8.03420	−	1.66178i	0.637153	−	0.131788i
$160$		−	4.07740i		−	0.322347i
$161$	−14.2334	−	10.9333i	−1.12175	−	0.861669i
$162$	−6.16725	+	6.55477i	−0.484545	+	0.514992i
$163$	7.80445	−	13.5177i	0.611292	−	1.05879i	−0.379731	−	0.925097i	$-0.623984\pi$
$163$	7.80445	−	13.5177i	0.611292	−	1.05879i	0.991023	−	0.133691i	$-0.0426831\pi$
$164$	−1.99215	−	3.45051i	−0.155561	−	0.269440i
$165$	5.04558	+	5.66578i	0.392798	+	0.441080i
$166$			0.0397535i			0.00308547i
$167$	3.87830	−	6.71742i	0.300112	−	0.519809i	−0.676049	−	0.736857i	$-0.736309\pi$
$167$	3.87830	−	6.71742i	0.300112	−	0.519809i	0.976161	+	0.217047i	$0.0696426\pi$
$168$	−2.57291	−	3.79211i	−0.198505	−	0.292568i
$169$	13.6950	+	23.7205i	1.05346	+	1.82465i
$170$	6.16514	−	10.6783i	0.472844	−	0.818990i
$171$	12.4064	−	4.13288i	0.948743	−	0.316049i
$172$	−3.14519	−	5.44764i	−0.239819	−	0.415378i
$173$	0.882084			0.0670636			0.0335318	−	0.999438i	$-0.489324\pi$
$173$	0.882084			0.0670636			0.0335318	+	0.999438i	$0.489324\pi$
$174$	−3.10102	+	9.36905i	−0.235088	+	0.710266i
$175$	11.7556	+	28.4222i	0.888643	+	2.14852i
$176$	−0.930342	+	0.537133i	−0.0701272	+	0.0404880i
$177$	4.53322	−	13.6961i	0.340737	−	1.02946i
$178$	−0.110424	−	0.191260i	−0.00827662	−	0.0143355i
$179$	−3.25659	−	5.64058i	−0.243409	−	0.421597i	0.718274	−	0.695760i	$-0.244932\pi$
$179$	−3.25659	−	5.64058i	−0.243409	−	0.421597i	−0.961683	+	0.274164i	$0.911599\pi$
$180$	4.85258	+	11.2285i	0.361690	+	0.836923i
$181$	16.7223	+	9.65465i	1.24296	+	0.717625i	0.969696	−	0.244314i	$-0.0785627\pi$
$181$	16.7223	+	9.65465i	1.24296	+	0.717625i	0.273266	+	0.961938i	$0.411896\pi$
$182$	−2.20337	+	16.6696i	−0.163325	+	1.23563i
$183$	−8.85693	−	9.94563i	−0.654723	−	0.735202i
$184$	−5.87482	+	3.39183i	−0.433098	+	0.250049i
$185$	−8.63413	+	14.9547i	−0.634794	+	1.09949i
$186$	−6.65621	+	5.92759i	−0.488057	+	0.434632i
$187$	−3.24864			−0.237564
$188$	−3.44099	+	1.98666i	−0.250960	+	0.144892i
$189$	11.5984	+	7.38080i	0.843663	+	0.536874i
$190$	1.53302	−	17.7067i	0.111217	−	1.28458i
$191$	7.77719	+	4.49016i	0.562737	+	0.324897i	0.754244	−	0.656595i	$-0.228004\pi$
$191$	7.77719	+	4.49016i	0.562737	+	0.324897i	−0.191506	+	0.981491i	$0.561337\pi$
$192$	−1.69615	+	0.350829i	−0.122409	+	0.0253189i
$193$	0.0705418	+	0.0407273i	0.00507771	+	0.00293162i	0.502537	−	0.864556i	$-0.332400\pi$
$193$	0.0705418	+	0.0407273i	0.00507771	+	0.00293162i	−0.497459	+	0.867487i	$0.665734\pi$
$194$	−12.0392	+	6.95084i	−0.864365	+	0.499041i
$195$	14.1032	−	42.6096i	1.00995	−	3.05134i
$196$	−4.95487	+	4.94462i	−0.353919	+	0.353187i
$197$			22.2690i			1.58660i	0.608830	+	0.793301i	$0.291639\pi$
$197$			22.2690i			1.58660i	−0.608830	+	0.793301i	$0.708361\pi$
$198$	1.92276	−	2.58639i	0.136645	−	0.183807i
$199$	3.50713			0.248614			0.124307	−	0.992244i	$-0.460329\pi$
$199$	3.50713			0.248614			0.124307	+	0.992244i	$0.460329\pi$
$200$	11.6252			0.822027
$201$	−2.66299	−	12.8747i	−0.187833	−	0.908112i
$202$		−	8.79633i		−	0.618907i
$203$	14.9450	+	1.97542i	1.04894	+	0.138647i
$204$	−4.97251	−	1.64583i	−0.348146	−	0.115231i
$205$	14.0691	−	8.12282i	0.982631	−	0.567322i
$206$	11.3862	+	6.57382i	0.793314	+	0.458020i
$207$	12.1416	−	16.3323i	0.843902	−	1.13517i
$208$	5.50387	+	3.17766i	0.381625	+	0.220331i
$209$	−4.24211	+	1.98279i	−0.293433	+	0.137153i
$210$	15.4620	−	10.4908i	1.06698	−	0.723934i
$211$	4.52926	−	2.61497i	0.311807	−	0.180022i	−0.335928	−	0.941888i	$-0.609050\pi$
$211$	4.52926	−	2.61497i	0.311807	−	0.180022i	0.647735	+	0.761866i	$0.275716\pi$
$212$	−4.73673			−0.325320
$213$	−10.0526	−	11.2883i	−0.688795	−	0.773462i
$214$	1.67647	−	2.90374i	0.114601	−	0.198495i
$215$	22.2122	−	12.8242i	1.51486	−	0.874605i
$216$	4.25339	−	2.98474i	0.289407	−	0.203086i
$217$	10.7971	+	8.29376i	0.732953	+	0.563017i
$218$	8.50939	+	4.91290i	0.576329	+	0.332743i
$219$	−4.56976	+	13.8065i	−0.308796	+	0.932958i
$220$	−2.19011	−	3.79338i	−0.147657	−	0.255750i
$221$	9.60940	+	16.6440i	0.646398	+	1.11959i
$222$	6.96389	+	2.30495i	0.467385	+	0.154698i
$223$	−6.31674	+	3.64697i	−0.423000	+	0.244219i	−0.696360	−	0.717693i	$-0.745198\pi$
$223$	−6.31674	+	3.64697i	−0.423000	+	0.244219i	0.273360	+	0.961912i	$0.411865\pi$
$224$	1.01122	+	2.44488i	0.0675650	+	0.163355i
$225$	−32.0139	+	13.8354i	−2.13426	+	0.922357i
$226$	11.3167			0.752775
$227$	0.329401	+	0.570539i	0.0218631	+	0.0378680i	0.876750	−	0.480946i	$-0.159707\pi$
$227$	0.329401	+	0.570539i	0.0218631	+	0.0378680i	−0.854887	+	0.518814i	$0.826374\pi$
$228$	−7.49769	+	0.885812i	−0.496547	+	0.0586643i
$229$	−0.556790	+	0.964389i	−0.0367937	+	0.0637286i	−0.883836	−	0.467797i	$-0.845048\pi$
$229$	−0.556790	+	0.964389i	−0.0367937	+	0.0637286i	0.847042	+	0.531526i	$0.178381\pi$
$230$	−13.8299	−	23.9540i	−0.911914	−	1.57948i
$231$	−4.43056	−	2.14596i	−0.291510	−	0.141194i
$232$	2.84891	−	4.93446i	0.187040	−	0.323963i
$233$			18.5403i			1.21461i	0.794468	+	0.607307i	$0.207750\pi$
$233$			18.5403i			1.21461i	−0.794468	+	0.607307i	$0.792250\pi$
$234$	−18.9385	−	2.20052i	−1.23805	−	0.143852i
$235$	−8.10039	−	14.0303i	−0.528411	−	0.915236i
$236$	−4.16467	+	7.21341i	−0.271097	+	0.469553i
$237$	−2.41368	−	11.6694i	−0.156785	−	0.758008i
$238$	−1.04843	+	7.93190i	−0.0679596	+	0.514148i
$239$		−	16.5866i		−	1.07290i	−0.843933	−	0.536448i	$-0.819766\pi$
$239$		−	16.5866i		−	1.07290i	0.843933	−	0.536448i	$-0.180234\pi$
$240$	−1.43047	−	6.91588i	−0.0923365	−	0.446418i
$241$			19.1897i			1.23612i	0.786131	+	0.618059i	$0.212081\pi$
$241$			19.1897i			1.23612i	−0.786131	+	0.618059i	$0.787919\pi$
$242$	4.92298	−	8.52684i	0.316461	−	0.548126i
$243$	−8.16096	+	13.2815i	−0.523526	+	0.852010i
$244$	3.84448	+	6.65884i	0.246118	+	0.426289i
$245$	−20.1612	−	20.2030i	−1.28805	−	1.29072i
$246$	−4.58953	−	5.15368i	−0.292618	−	0.328586i
$247$	22.7067	+	15.8688i	1.44479	+	1.00971i
$248$	4.45649	−	2.57296i	0.282988	−	0.163383i
$249$	0.0139467	+	0.0674279i	0.000883835	+	0.00427307i
$250$			27.0137i			1.70849i
$251$	2.51541	+	1.45227i	0.158771	+	0.0916666i	0.577280	−	0.816546i	$-0.304114\pi$
$251$	2.51541	+	1.45227i	0.158771	+	0.0916666i	−0.418509	+	0.908213i	$0.637447\pi$
$252$	−5.69443	−	5.52933i	−0.358715	−	0.348315i
$253$	−3.64373	+	6.31113i	−0.229079	+	0.396777i
$254$	−10.5158	−	6.07128i	−0.659818	−	0.380946i
$255$	6.71072	−	20.2749i	0.420241	−	1.26967i
$256$	1.00000			0.0625000
$257$	−10.6628	−	18.4686i	−0.665130	−	1.15204i	−0.979250	−	0.202656i	$-0.935043\pi$
$257$	−10.6628	−	18.4686i	−0.665130	−	1.15204i	0.314120	−	0.949383i	$-0.398291\pi$
$258$	−7.24591	−	8.13657i	−0.451110	−	0.506561i
$259$	1.46830	−	11.1084i	0.0912358	−	0.690244i
$260$	−12.9566	+	22.4415i	−0.803534	+	1.39176i
$261$	−1.97286	+	16.9792i	−0.122117	+	1.05099i
$262$		−	12.7980i		−	0.790665i
$263$	24.8822	+	14.3657i	1.53430	+	0.885830i	0.999156	+	0.0410697i	$0.0130766\pi$
$263$	24.8822	+	14.3657i	1.53430	+	0.885830i	0.535146	+	0.844760i	$0.320257\pi$
$264$	−1.38956	+	1.23745i	−0.0855213	+	0.0761597i
$265$		−	19.3136i		−	1.18642i
$266$	3.47215	+	10.9975i	0.212891	+	0.674298i
$267$	−0.254395	−	0.285665i	−0.0155687	−	0.0174824i
$268$			7.59056i			0.463667i
$269$	−3.16236	+	5.47737i	−0.192812	+	0.333961i	−0.946181	−	0.323637i	$-0.895094\pi$
$269$	−3.16236	+	5.47737i	−0.192812	+	0.333961i	0.753369	+	0.657598i	$0.228428\pi$
$270$	12.1700	+	17.3428i	0.740642	+	1.05545i
$271$	−11.2321			−0.682301			−0.341150	−	0.940009i	$-0.610817\pi$
$271$	−11.2321			−0.682301			−0.341150	+	0.940009i	$0.610817\pi$
$272$	2.61890	+	1.51203i	0.158794	+	0.0916800i
$273$	2.11094	+	29.0471i	0.127760	+	1.75801i
$274$			17.3126i			1.04589i
$275$	10.8154	−	6.24429i	0.652195	−	0.376545i
$276$	−8.77462	+	7.81411i	−0.528170	+	0.470354i
$277$	6.94047	+	12.0212i	0.417012	+	0.722287i	0.995637	−	0.0933070i	$-0.0297438\pi$
$277$	6.94047	+	12.0212i	0.417012	+	0.722287i	−0.578625	+	0.815594i	$0.696410\pi$
$278$	−0.616575	+	1.06794i	−0.0369797	+	0.0640508i
$279$	−9.21034	+	12.3893i	−0.551409	+	0.741725i
$280$	−9.96876	+	4.12315i	−0.595747	+	0.246405i
$281$	4.96581	−	8.60104i	0.296235	−	0.513095i	−0.679036	−	0.734105i	$-0.737602\pi$
$281$	4.96581	−	8.60104i	0.296235	−	0.513095i	0.975272	+	0.221010i	$0.0709354\pi$
$282$	−5.13945	+	4.57686i	−0.306050	+	0.272548i
$283$	2.44319	−	4.23173i	0.145233	−	0.251550i	−0.784227	−	0.620474i	$-0.786940\pi$
$283$	2.44319	−	4.23173i	0.145233	−	0.251550i	0.929460	+	0.368924i	$0.120274\pi$
$284$	4.36350	+	7.55780i	0.258926	+	0.448473i
$285$	−3.61181	−	30.5711i	−0.213945	−	1.81088i
$286$	6.82731			0.403707
$287$	−6.42158	+	8.35980i	−0.379054	+	0.493464i
$288$	−2.75384	+	1.19012i	−0.162271	+	0.0701283i
$289$	−3.92756	−	6.80273i	−0.231033	−	0.400161i
$290$	20.1198	+	11.6162i	1.18147	+	0.682124i
$291$	−17.9817	+	16.0134i	−1.05411	+	0.938720i
$292$	4.19824	−	7.27157i	0.245684	−	0.425536i
$293$	−5.22364			−0.305168			−0.152584	−	0.988290i	$-0.548759\pi$
$293$	−5.22364			−0.305168			−0.152584	+	0.988290i	$0.548759\pi$
$294$	−6.66947	+	10.1251i	−0.388972	+	0.590509i
$295$	−29.4120	−	16.9810i	−1.71243	−	0.988673i
$296$	−3.66771	−	2.11756i	−0.213182	−	0.123080i
$297$	2.35391	−	5.06147i	0.136587	−	0.293696i
$298$			17.8685i			1.03510i
$299$	43.1123			2.49325
$300$	19.7181	−	4.07846i	1.13842	−	0.235470i
$301$	−10.1383	+	13.1984i	−0.584364	+	0.760742i
$302$	17.6780	−	10.2064i	1.01726	−	0.587313i
$303$	−3.08601	−	14.9199i	−0.177286	−	0.857124i
$304$	4.34265	+	0.375980i	0.249068	+	0.0215639i
$305$	−27.1508	+	15.6755i	−1.55465	+	0.897577i
$306$	−9.01153	−	1.04707i	−0.515155	−	0.0598571i
$307$	−5.40797	+	3.12229i	−0.308649	+	0.178199i	−0.646322	−	0.763065i	$-0.723694\pi$
$307$	−5.40797	+	3.12229i	−0.308649	+	0.178199i	0.337673	+	0.941264i	$0.390360\pi$
$308$	2.25401	+	1.73141i	0.128434	+	0.0986565i
$309$	21.6190	+	7.15557i	1.22986	+	0.407066i
$310$	10.4910	+	18.1709i	0.595848	+	1.03204i
$311$	13.4139	−	7.74450i	0.760631	−	0.439151i	−0.0688913	−	0.997624i	$-0.521946\pi$
$311$	13.4139	−	7.74450i	0.760631	−	0.439151i	0.829522	+	0.558474i	$0.188613\pi$
$312$	10.4502	+	3.45886i	0.591625	+	0.195820i
$313$	2.62607	+	4.54849i	0.148434	+	0.257096i	0.930649	−	0.365913i	$-0.119243\pi$
$313$	2.62607	+	4.54849i	0.148434	+	0.257096i	−0.782215	+	0.623009i	$0.785910\pi$
$314$	−7.34628	+	12.7241i	−0.414575	+	0.718064i
$315$	22.5453	−	23.2185i	1.27028	−	1.30821i
$316$			6.87993i			0.387026i
$317$	−4.04167	−	7.00037i	−0.227003	−	0.393180i	0.729916	−	0.683537i	$-0.239559\pi$
$317$	−4.04167	−	7.00037i	−0.227003	−	0.393180i	−0.956918	+	0.290357i	$0.906226\pi$
$318$	−8.03420	+	1.66178i	−0.450535	+	0.0931882i
$319$		−	6.12098i		−	0.342709i
$320$			4.07740i			0.227934i
$321$	1.82483	−	5.51332i	0.101852	−	0.307724i
$322$	14.2334	+	10.9333i	0.793194	+	0.609292i
$323$	10.8045	+	7.55086i	0.601179	+	0.420141i
$324$	6.16725	−	6.55477i	0.342625	−	0.364154i
$325$	−63.9836	−	36.9410i	−3.54917	−	2.04912i
$326$	−7.80445	+	13.5177i	−0.432248	+	0.748676i
$327$	16.1568	+	5.34766i	0.893472	+	0.295726i
$328$	1.99215	+	3.45051i	0.109998	+	0.190523i
$329$	8.33673	+	6.40385i	0.459619	+	0.353056i
$330$	−5.04558	−	5.66578i	−0.277750	−	0.311891i
$331$	−21.1450	−	12.2081i	−1.16223	−	0.671016i	−0.210396	−	0.977616i	$-0.567475\pi$
$331$	−21.1450	−	12.2081i	−1.16223	−	0.671016i	−0.951838	+	0.306600i	$0.900809\pi$
$332$		−	0.0397535i		−	0.00218176i
$333$	12.6204	+	1.46640i	0.691595	+	0.0803582i
$334$	−3.87830	+	6.71742i	−0.212211	+	0.367561i
$335$	−30.9497			−1.69097
$336$	2.57291	+	3.79211i	0.140364	+	0.206877i
$337$	7.76773	−	4.48470i	0.423135	−	0.244297i	−0.273283	−	0.961934i	$-0.588109\pi$
$337$	7.76773	−	4.48470i	0.423135	−	0.244297i	0.696418	+	0.717637i	$0.254776\pi$
$338$	−13.6950	−	23.7205i	−0.744912	−	1.29022i
$339$	19.1948	−	3.97022i	1.04252	−	0.215633i
$340$	−6.16514	+	10.6783i	−0.334351	+	0.579114i
$341$	2.76404	−	4.78746i	0.149681	−	0.259256i
$342$	−12.4064	+	4.13288i	−0.670863	+	0.223480i
$343$	17.0995	+	7.11395i	0.923284	+	0.384117i
$344$	3.14519	+	5.44764i	0.169578	+	0.293717i
$345$	−31.8613	−	35.7777i	−1.71535	−	1.92620i
$346$	−0.882084			−0.0474211
$347$	−15.1730	−	8.76013i	−0.814529	−	0.470268i	0.0339974	−	0.999422i	$-0.489176\pi$
$347$	−15.1730	−	8.76013i	−0.814529	−	0.470268i	−0.848526	+	0.529154i	$0.822510\pi$
$348$	3.10102	−	9.36905i	0.166232	−	0.502234i
$349$	−7.55071			−0.404180			−0.202090	−	0.979367i	$-0.564773\pi$
$349$	−7.55071			−0.404180			−0.202090	+	0.979367i	$0.564773\pi$
$350$	−11.7556	−	28.4222i	−0.628366	−	1.51923i
$351$	−32.8946	+	2.91179i	−1.75578	+	0.155420i
$352$	0.930342	−	0.537133i	0.0495874	−	0.0286293i
$353$	−18.3795	+	10.6114i	−0.978243	+	0.564789i	−0.901739	−	0.432280i	$-0.857709\pi$
$353$	−18.3795	+	10.6114i	−0.978243	+	0.564789i	−0.0765039	+	0.997069i	$0.524376\pi$
$354$	−4.53322	+	13.6961i	−0.240938	+	0.727940i
$355$	−30.8162	+	17.7917i	−1.63555	+	0.944287i
$356$	0.110424	+	0.191260i	0.00585245	+	0.0101367i
$357$	1.00445	+	13.8215i	0.0531610	+	0.731511i
$358$	3.25659	+	5.64058i	0.172116	+	0.298114i
$359$		−	14.7462i		−	0.778272i	−0.921180	−	0.389136i	$-0.872774\pi$
$359$		−	14.7462i		−	0.778272i	0.921180	−	0.389136i	$-0.127226\pi$
$360$	−4.85258	−	11.2285i	−0.255754	−	0.591794i
$361$	18.7173	+	3.26550i	0.985120	+	0.171868i
$362$	−16.7223	−	9.65465i	−0.878907	−	0.507437i
$363$	5.35863	−	16.1899i	0.281255	−	0.849750i
$364$	2.20337	−	16.6696i	0.115488	−	0.873725i
$365$	29.6491	+	17.1179i	1.55191	+	0.895993i
$366$	8.85693	+	9.94563i	0.462959	+	0.519866i
$367$	24.9894			1.30443			0.652217	−	0.758033i	$-0.273839\pi$
$367$	24.9894			1.30443			0.652217	+	0.758033i	$0.273839\pi$
$368$	5.87482	−	3.39183i	0.306246	−	0.176811i
$369$	−9.59258	−	7.13126i	−0.499370	−	0.371238i
$370$	8.63413	−	14.9547i	0.448867	−	0.777460i
$371$	4.78988	+	11.5807i	0.248678	+	0.601242i
$372$	6.65621	−	5.92759i	0.345108	−	0.307331i
$373$	−4.75225	−	2.74372i	−0.246062	−	0.142064i	0.371898	−	0.928274i	$-0.378707\pi$
$373$	−4.75225	−	2.74372i	−0.246062	−	0.142064i	−0.617960	+	0.786210i	$0.712041\pi$
$374$	3.24864			0.167983
$375$	9.47717	+	45.8192i	0.489399	+	2.36609i
$376$	3.44099	−	1.98666i	0.177455	−	0.102454i
$377$	−31.3600	+	18.1057i	−1.61512	+	0.932493i
$378$	−11.5984	−	7.38080i	−0.596559	−	0.379627i
$379$			20.9015i			1.07364i	0.843697	+	0.536820i	$0.180374\pi$
$379$			20.9015i			1.07364i	−0.843697	+	0.536820i	$0.819626\pi$
$380$	−1.53302	+	17.7067i	−0.0786423	+	0.908337i
$381$	−19.9663	−	6.60855i	−1.02290	−	0.338566i
$382$	−7.77719	−	4.49016i	−0.397915	−	0.229737i
$383$	19.1265			0.977318			0.488659	−	0.872475i	$-0.337486\pi$
$383$	19.1265			0.977318			0.488659	+	0.872475i	$0.337486\pi$
$384$	1.69615	−	0.350829i	0.0865562	−	0.0179032i
$385$	−7.05967	+	9.19049i	−0.359794	+	0.468391i
$386$	−0.0705418	−	0.0407273i	−0.00359048	−	0.00207297i
$387$	−15.1447	−	11.2588i	−0.769847	−	0.572315i
$388$	12.0392	−	6.95084i	0.611198	−	0.352876i
$389$		−	30.6695i		−	1.55500i	−0.628880	−	0.777502i	$-0.716487\pi$
$389$		−	30.6695i		−	1.55500i	0.628880	−	0.777502i	$-0.283513\pi$
$390$	−14.1032	+	42.6096i	−0.714142	+	2.15762i
$391$	20.5141			1.03744
$392$	4.95487	−	4.94462i	0.250259	−	0.249741i
$393$	−4.48992	−	21.7074i	−0.226486	−	1.09499i
$394$		−	22.2690i		−	1.12190i
$395$	−28.0522			−1.41146
$396$	−1.92276	+	2.58639i	−0.0966224	+	0.129971i
$397$	13.3341			0.669221			0.334610	−	0.942357i	$-0.391395\pi$
$397$	13.3341			0.669221			0.334610	+	0.942357i	$0.391395\pi$
$398$	−3.50713			−0.175796
$399$	9.74752	+	17.4352i	0.487986	+	0.872851i
$400$	−11.6252			−0.581261
$401$	−2.19502			−0.109614			−0.0548070	−	0.998497i	$-0.517454\pi$
$401$	−2.19502			−0.109614			−0.0548070	+	0.998497i	$0.517454\pi$
$402$	2.66299	+	12.8747i	0.132818	+	0.642132i
$403$	−32.7039			−1.62910
$404$			8.79633i			0.437634i
$405$	26.7265	+	25.1463i	1.32805	+	1.24953i
$406$	−14.9450	−	1.97542i	−0.741709	−	0.0980384i
$407$	−4.54964			−0.225517
$408$	4.97251	+	1.64583i	0.246176	+	0.0814808i
$409$			3.79885i			0.187841i	0.995580	+	0.0939204i	$0.0299399\pi$
$409$			3.79885i			0.187841i	−0.995580	+	0.0939204i	$0.970060\pi$
$410$	−14.0691	+	8.12282i	−0.694825	+	0.401157i
$411$	6.07375	+	29.3647i	0.299596	+	1.44845i
$412$	−11.3862	−	6.57382i	−0.560958	−	0.323869i
$413$	21.8473	+	2.88776i	1.07504	+	0.142097i
$414$	−12.1416	+	16.3323i	−0.596729	+	0.802688i
$415$	0.162091			0.00795674
$416$	−5.50387	−	3.17766i	−0.269849	−	0.155798i
$417$	−0.671139	+	2.02770i	−0.0328658	+	0.0992967i
$418$	4.24211	−	1.98279i	0.207488	−	0.0969816i
$419$		−	16.5211i		−	0.807108i	−0.914956	−	0.403554i	$-0.867775\pi$
$419$		−	16.5211i		−	0.807108i	0.914956	−	0.403554i	$-0.132225\pi$
$420$	−15.4620	+	10.4908i	−0.754467	+	0.511899i
$421$	7.50592	−	4.33355i	0.365816	−	0.211204i	−0.305813	−	0.952092i	$-0.598928\pi$
$421$	7.50592	−	4.33355i	0.365816	−	0.211204i	0.671629	+	0.740888i	$0.265595\pi$
$422$	−4.52926	+	2.61497i	−0.220481	+	0.127295i
$423$	−7.11157	+	9.56610i	−0.345777	+	0.465120i
$424$	4.73673			0.230036
$425$	−30.4453	−	17.5776i	−1.47681	−	0.852640i
$426$	10.0526	+	11.2883i	0.487052	+	0.546920i
$427$	12.3924	−	16.1329i	0.599712	−	0.780724i
$428$	−1.67647	+	2.90374i	−0.0810354	+	0.140357i
$429$	11.5801	−	2.39522i	0.559094	−	0.115642i
$430$	−22.2122	+	12.8242i	−1.07117	+	0.618439i
$431$	−4.88374			−0.235241			−0.117621	−	0.993059i	$-0.537527\pi$
$431$	−4.88374			−0.235241			−0.117621	+	0.993059i	$0.537527\pi$
$432$	−4.25339	+	2.98474i	−0.204641	+	0.143603i
$433$	9.13958	+	5.27674i	0.439220	+	0.253584i	0.703267	−	0.710926i	$-0.251724\pi$
$433$	9.13958	+	5.27674i	0.439220	+	0.253584i	−0.264047	+	0.964510i	$0.585057\pi$
$434$	−10.7971	−	8.29376i	−0.518276	−	0.398113i
$435$	38.2014	+	12.6441i	1.83162	+	0.606239i
$436$	−8.50939	−	4.91290i	−0.407526	−	0.235285i
$437$	26.7876	−	12.5207i	1.28142	−	0.598948i
$438$	4.56976	−	13.8065i	0.218352	−	0.659701i
$439$		−	9.52603i		−	0.454652i	−0.973819	−	0.227326i	$-0.927002\pi$
$439$		−	9.52603i		−	0.454652i	0.973819	−	0.227326i	$-0.0729984\pi$
$440$	2.19011	+	3.79338i	0.104409	+	0.180842i
$441$	−7.76023	+	19.5136i	−0.369535	+	0.929217i
$442$	−9.60940	−	16.6440i	−0.457073	−	0.791673i
$443$	−25.2198	+	14.5607i	−1.19823	+	0.691798i	−0.960160	−	0.279450i	$-0.909848\pi$
$443$	−25.2198	+	14.5607i	−1.19823	+	0.691798i	−0.238069	+	0.971248i	$0.576514\pi$
$444$	−6.96389	−	2.30495i	−0.330491	−	0.109388i
$445$	−0.779843	+	0.450242i	−0.0369681	+	0.0213435i
$446$	6.31674	−	3.64697i	0.299106	−	0.172689i
$447$	6.26880	+	30.3077i	0.296504	+	1.43350i
$448$	−1.01122	−	2.44488i	−0.0477757	−	0.115510i
$449$	37.7884			1.78335			0.891674	−	0.452679i	$-0.149532\pi$
$449$	37.7884			1.78335			0.891674	+	0.452679i	$0.149532\pi$
$450$	32.0139	−	13.8354i	1.50915	−	0.652205i
$451$	3.70677	+	2.14011i	0.174545	+	0.100774i
$452$	−11.3167			−0.532292
$453$	26.4038	−	23.5135i	1.24056	−	1.10476i
$454$	−0.329401	−	0.570539i	−0.0154595	−	0.0267767i
$455$	67.9687	+	8.98403i	3.18642	+	0.421178i
$456$	7.49769	−	0.885812i	0.351111	−	0.0414819i
$457$	−2.19166	+	3.79607i	−0.102522	+	0.177572i	−0.912723	−	0.408579i	$-0.866024\pi$
$457$	−2.19166	+	3.79607i	−0.102522	+	0.177572i	0.810201	+	0.586152i	$0.199358\pi$
$458$	0.556790	−	0.964389i	0.0260171	−	0.0450629i
$459$	−15.6522	+	1.38552i	−0.730583	+	0.0646703i
$460$	13.8299	+	23.9540i	0.644821	+	1.11686i
$461$	−11.0809	+	6.39758i	−0.516091	+	0.297965i	−0.735334	−	0.677705i	$-0.762975\pi$
$461$	−11.0809	+	6.39758i	−0.516091	+	0.297965i	0.219243	+	0.975670i	$0.429641\pi$
$462$	4.43056	+	2.14596i	0.206128	+	0.0998393i
$463$	1.81932			0.0845510			0.0422755	−	0.999106i	$-0.486539\pi$
$463$	1.81932			0.0845510			0.0422755	+	0.999106i	$0.486539\pi$
$464$	−2.84891	+	4.93446i	−0.132257	+	0.229076i
$465$	24.1692	+	27.1400i	1.12082	+	1.25859i
$466$		−	18.5403i		−	0.858861i
$467$	−15.3869	−	8.88363i	−0.712021	−	0.411085i	0.0997880	−	0.995009i	$-0.468184\pi$
$467$	−15.3869	−	8.88363i	−0.712021	−	0.411085i	−0.811809	+	0.583923i	$0.801517\pi$
$468$	18.9385	+	2.20052i	0.875434	+	0.101719i
$469$	18.5580	−	7.67572i	0.856928	−	0.354432i
$470$	8.10039	+	14.0303i	0.373643	+	0.647169i
$471$	−7.99639	+	24.1593i	−0.368454	+	1.11320i
$472$	4.16467	−	7.21341i	0.191694	−	0.332024i
$473$	5.85222	+	3.37878i	0.269085	+	0.155356i
$474$	2.41368	+	11.6694i	0.110864	+	0.535992i
$475$	−50.4843	−	4.37084i	−2.31638	−	0.200548i
$476$	1.04843	−	7.93190i	0.0480547	−	0.363558i
$477$	−13.0442	+	5.63726i	−0.597252	+	0.258112i
$478$			16.5866i			0.758652i
$479$			14.5072i			0.662849i	0.943482	+	0.331425i	$0.107529\pi$
$479$			14.5072i			0.662849i	−0.943482	+	0.331425i	$0.892471\pi$
$480$	1.43047	+	6.91588i	0.0652918	+	0.315665i
$481$	13.4577	+	23.3095i	0.613620	+	1.06282i
$482$		−	19.1897i		−	0.874068i
$483$	27.9776	+	13.5511i	1.27303	+	0.616597i
$484$	−4.92298	+	8.52684i	−0.223772	+	0.387584i
$485$	28.3414	+	49.0887i	1.28692	+	2.22900i
$486$	8.16096	−	13.2815i	0.370189	−	0.602462i
$487$	2.57977	−	1.48943i	0.116900	−	0.0674925i	−0.440410	−	0.897797i	$-0.645167\pi$
$487$	2.57977	−	1.48943i	0.116900	−	0.0674925i	0.557310	+	0.830304i	$0.311833\pi$
$488$	−3.84448	−	6.65884i	−0.174032	−	0.301432i
$489$	−8.49510	+	25.6661i	−0.384162	+	1.16066i
$490$	20.1612	+	20.2030i	0.910791	+	0.912678i
$491$	21.7386	−	12.5508i	0.981048	−	0.566409i	0.0784619	−	0.996917i	$-0.474999\pi$
$491$	21.7386	−	12.5508i	0.981048	−	0.566409i	0.902586	+	0.430509i	$0.141666\pi$
$492$	4.58953	+	5.15368i	0.206912	+	0.232346i
$493$	−14.9221	+	8.61525i	−0.672055	+	0.388011i
$494$	−22.7067	−	15.8688i	−1.02162	−	0.713972i
$495$	−10.5458	−	7.83987i	−0.473997	−	0.352376i
$496$	−4.45649	+	2.57296i	−0.200103	+	0.115529i
$497$	14.0654	−	18.3108i	0.630922	−	0.821353i
$498$	−0.0139467	−	0.0674279i	−0.000624966	−	0.00302151i
$499$	−20.7249			−0.927773			−0.463887	−	0.885895i	$-0.653546\pi$
$499$	−20.7249			−0.927773			−0.463887	+	0.885895i	$0.653546\pi$
$500$		−	27.0137i		−	1.20809i
$501$	−4.22151	+	12.7544i	−0.188603	+	0.569823i
$502$	−2.51541	−	1.45227i	−0.112268	−	0.0648181i
$503$	19.8551	+	11.4633i	0.885294	+	0.511125i	0.872400	−	0.488792i	$-0.162562\pi$
$503$	19.8551	+	11.4633i	0.885294	+	0.511125i	0.0128938	+	0.999917i	$0.495896\pi$
$504$	5.69443	+	5.52933i	0.253650	+	0.246296i
$505$	−35.8662			−1.59602
$506$	3.64373	−	6.31113i	0.161984	−	0.280564i
$507$	−31.5506	−	35.4289i	−1.40121	−	1.57345i
$508$	10.5158	+	6.07128i	0.466562	+	0.269369i
$509$	14.5868	+	25.2651i	0.646549	+	1.11986i	0.983941	+	0.178492i	$0.0571219\pi$
$509$	14.5868	+	25.2651i	0.646549	+	1.11986i	−0.337392	+	0.941364i	$0.609545\pi$
$510$	−6.71072	+	20.2749i	−0.297156	+	0.897789i
$511$	−22.0235	−	2.91104i	−0.974260	−	0.128777i
$512$	−1.00000			−0.0441942
$513$	−19.5932	+	11.3625i	−0.865061	+	0.501667i
$514$	10.6628	+	18.4686i	0.470318	+	0.814614i
$515$	26.8041	−	46.4261i	1.18113	−	2.04578i
$516$	7.24591	+	8.13657i	0.318983	+	0.358193i
$517$	2.13420	−	3.69654i	0.0938619	−	0.162574i
$518$	−1.46830	+	11.1084i	−0.0645135	+	0.488076i
$519$	−1.49614	+	0.309461i	−0.0656735	+	0.0135838i
$520$	12.9566	−	22.4415i	0.568184	−	0.984124i
$521$	5.56777	+	9.64365i	0.243928	+	0.422496i	0.961830	−	0.273649i	$-0.0882305\pi$
$521$	5.56777	+	9.64365i	0.243928	+	0.422496i	−0.717902	+	0.696145i	$0.754897\pi$
$522$	1.97286	−	16.9792i	0.0863497	−	0.743161i
$523$	10.3965	−	6.00242i	0.454607	−	0.262467i	−0.255167	−	0.966897i	$-0.582130\pi$
$523$	10.3965	−	6.00242i	0.454607	−	0.262467i	0.709774	+	0.704430i	$0.248797\pi$
$524$			12.7980i			0.559084i
$525$	−29.9107	−	44.0841i	−1.30541	−	1.92399i
$526$	−24.8822	−	14.3657i	−1.08492	−	0.626376i
$527$	−15.5615			−0.677870
$528$	1.38956	−	1.23745i	0.0604727	−	0.0538531i
$529$	11.5090	−	19.9342i	0.500393	−	0.866706i
$530$			19.3136i			0.838927i
$531$	−2.88402	+	24.8210i	−0.125156	+	1.07714i
$532$	−3.47215	−	10.9975i	−0.150537	−	0.476800i
$533$		−	25.3216i		−	1.09680i
$534$	0.254395	+	0.285665i	0.0110087	+	0.0123619i
$535$	−11.8397	−	6.83565i	−0.511875	−	0.295531i
$536$		−	7.59056i		−	0.327862i
$537$	7.50254	+	8.42475i	0.323758	+	0.363555i
$538$	3.16236	−	5.47737i	0.136339	−	0.236146i
$539$	1.95380	−	7.26162i	0.0841562	−	0.312780i
$540$	−12.1700	−	17.3428i	−0.523713	−	0.746315i
$541$	0.439116	+	0.760571i	0.0188791	+	0.0326995i	0.875311	−	0.483561i	$-0.160657\pi$
$541$	0.439116	+	0.760571i	0.0188791	+	0.0326995i	−0.856432	+	0.516261i	$0.827324\pi$
$542$	11.2321			0.482459
$543$	−31.7507	−	10.5090i	−1.36255	−	0.450986i
$544$	−2.61890	−	1.51203i	−0.112285	−	0.0648276i
$545$	20.0319	−	34.6962i	0.858071	−	1.48622i
$546$	−2.11094	−	29.0471i	−0.0903397	−	1.24310i
$547$	24.5555	+	14.1771i	1.04992	+	0.606171i	0.922626	−	0.385695i	$-0.126038\pi$
$547$	24.5555	+	14.1771i	1.04992	+	0.606171i	0.127292	+	0.991865i	$0.459372\pi$
$548$		−	17.3126i		−	0.739556i
$549$	18.5119	+	13.7620i	0.790068	+	0.587347i
$550$	−10.8154	+	6.24429i	−0.461171	+	0.266257i
$551$	−14.2271	+	20.3575i	−0.606094	+	0.867259i
$552$	8.77462	−	7.81411i	0.373473	−	0.332591i
$553$	16.8206	−	6.95712i	0.715284	−	0.295847i
$554$	−6.94047	−	12.0212i	−0.294872	−	0.510734i
$555$	9.39820	−	28.3946i	0.398931	−	1.20528i
$556$	0.616575	−	1.06794i	0.0261486	−	0.0452907i
$557$		−	20.4332i		−	0.865783i	−0.901446	−	0.432891i	$-0.857493\pi$
$557$		−	20.4332i		−	0.865783i	0.901446	−	0.432891i	$-0.142507\pi$
$558$	9.21034	−	12.3893i	0.389905	−	0.524479i
$559$		−	39.9774i		−	1.69087i
$560$	9.96876	−	4.12315i	0.421257	−	0.174235i
$561$	5.51017	−	1.13972i	0.232640	−	0.0481189i
$562$	−4.96581	+	8.60104i	−0.209470	+	0.362813i
$563$	5.63759	+	9.76458i	0.237596	+	0.411528i	0.960024	−	0.279918i	$-0.0903073\pi$
$563$	5.63759	+	9.76458i	0.237596	+	0.411528i	−0.722428	+	0.691446i	$0.756974\pi$
$564$	5.13945	−	4.57686i	0.216410	−	0.192721i
$565$		−	46.1427i		−	1.94124i
$566$	−2.44319	+	4.23173i	−0.102695	+	0.177873i
$567$	−22.2621	−	8.44985i	−0.934919	−	0.354860i
$568$	−4.36350	−	7.55780i	−0.183088	−	0.317118i
$569$	10.4034	−	18.0192i	0.436133	−	0.755404i	−0.561254	−	0.827643i	$-0.689681\pi$
$569$	10.4034	−	18.0192i	0.436133	−	0.755404i	0.997387	+	0.0722389i	$0.0230144\pi$
$570$	3.61181	+	30.5711i	0.151282	+	1.28048i
$571$	−4.73612	−	8.20320i	−0.198201	−	0.343293i	0.749744	−	0.661727i	$-0.230176\pi$
$571$	−4.73612	−	8.20320i	−0.198201	−	0.343293i	−0.947945	+	0.318434i	$0.896843\pi$
$572$	−6.82731			−0.285464
$573$	−14.7665	−	4.88752i	−0.616881	−	0.204179i
$574$	6.42158	−	8.35980i	0.268032	−	0.348931i
$575$	−68.2961	+	39.4308i	−2.84814	+	1.64438i
$576$	2.75384	−	1.19012i	0.114743	−	0.0495882i
$577$	13.2596	+	22.9664i	0.552006	+	0.956102i	0.998130	+	0.0611311i	$0.0194708\pi$
$577$	13.2596	+	22.9664i	0.552006	+	0.956102i	−0.446124	+	0.894971i	$0.647196\pi$
$578$	3.92756	+	6.80273i	0.163365	+	0.282956i
$579$	−0.133938	−	0.0443315i	−0.00556626	−	0.00184235i
$580$	−20.1198	−	11.6162i	−0.835428	−	0.482335i
$581$	−0.0971925	+	0.0401996i	−0.00403223	+	0.00166776i
$582$	17.9817	−	16.0134i	0.745367	−	0.663775i
$583$	4.40678	−	2.54426i	0.182510	−	0.105372i
$584$	−4.19824	+	7.27157i	−0.173724	+	0.300900i
$585$	−8.97239	+	77.2201i	−0.370963	+	3.19266i
$586$	5.22364			0.215786
$587$	−1.60097	+	0.924319i	−0.0660790	+	0.0381507i	−0.532675	−	0.846320i	$-0.678813\pi$
$587$	−1.60097	+	0.924319i	−0.0660790	+	0.0381507i	0.466597	+	0.884470i	$0.345480\pi$
$588$	6.66947	−	10.1251i	0.275044	−	0.417553i
$589$	−20.3204	+	9.49792i	−0.837287	+	0.391355i
$590$	29.4120	+	16.9810i	1.21087	+	0.699098i
$591$	−7.81262	−	37.7716i	−0.321368	−	1.55371i
$592$	3.66771	+	2.11756i	0.150742	+	0.0870310i
$593$	14.9410	−	8.62619i	0.613553	−	0.354235i	−0.160802	−	0.986987i	$-0.551408\pi$
$593$	14.9410	−	8.62619i	0.613553	−	0.354235i	0.774355	+	0.632752i	$0.218075\pi$
$594$	−2.35391	+	5.06147i	−0.0965819	+	0.207675i
$595$	32.3415	+	4.27487i	1.32587	+	0.175253i
$596$		−	17.8685i		−	0.731923i
$597$	−5.94861	+	1.23040i	−0.243460	+	0.0503570i
$598$	−43.1123			−1.76299
$599$	−37.2669			−1.52268			−0.761341	−	0.648351i	$-0.775459\pi$
$599$	−37.2669			−1.52268			−0.761341	+	0.648351i	$0.775459\pi$
$600$	−19.7181	+	4.07846i	−0.804987	+	0.166503i
$601$			40.1070i			1.63600i	0.575219	+	0.817999i	$0.304917\pi$
$601$			40.1070i			1.63600i	−0.575219	+	0.817999i	$0.695083\pi$
$602$	10.1383	−	13.1984i	0.413207	−	0.537926i
$603$	9.03364	+	20.9032i	0.367878	+	0.851242i
$604$	−17.6780	+	10.2064i	−0.719308	+	0.415293i
$605$	−34.7674	−	20.0730i	−1.41349	−	0.816082i
$606$	3.08601	+	14.9199i	0.125360	+	0.606078i
$607$	10.0993	+	5.83086i	0.409920	+	0.236667i	0.690755	−	0.723089i	$-0.257278\pi$
$607$	10.0993	+	5.83086i	0.409920	+	0.236667i	−0.280836	+	0.959756i	$0.590612\pi$
$608$	−4.34265	−	0.375980i	−0.176118	−	0.0152480i
$609$	−26.0420	+	1.89255i	−1.05528	+	0.0766899i
$610$	27.1508	−	15.6755i	1.09930	−	0.634683i
$611$	−25.2517			−1.02157
$612$	9.01153	+	1.04707i	0.364269	+	0.0423254i
$613$	−16.8208	+	29.1346i	−0.679388	+	1.17673i	0.295778	+	0.955257i	$0.404421\pi$
$613$	−16.8208	+	29.1346i	−0.679388	+	1.17673i	−0.975166	+	0.221477i	$0.928912\pi$
$614$	5.40797	−	3.12229i	0.218248	−	0.126006i
$615$	−21.0136	+	18.7134i	−0.847351	+	0.754595i
$616$	−2.25401	−	1.73141i	−0.0908165	−	0.0697607i
$617$	−2.35772	−	1.36123i	−0.0949181	−	0.0548010i	0.451790	−	0.892125i	$-0.350786\pi$
$617$	−2.35772	−	1.36123i	−0.0949181	−	0.0548010i	−0.546708	+	0.837324i	$0.684119\pi$
$618$	−21.6190	−	7.15557i	−0.869642	−	0.287839i
$619$	2.21738	+	3.84062i	0.0891240	+	0.154367i	0.907141	−	0.420827i	$-0.138260\pi$
$619$	2.21738	+	3.84062i	0.0891240	+	0.154367i	−0.818017	+	0.575194i	$0.804927\pi$
$620$	−10.4910	−	18.1709i	−0.421328	−	0.729762i
$621$	−14.8642	+	31.9616i	−0.596479	+	1.28258i
$622$	−13.4139	+	7.74450i	−0.537847	+	0.310526i
$623$	0.355944	−	0.463379i	0.0142606	−	0.0185649i
$624$	−10.4502	−	3.45886i	−0.418342	−	0.138465i
$625$	52.0195			2.08078
$626$	−2.62607	−	4.54849i	−0.104959	−	0.181794i
$627$	6.49962	−	4.85137i	0.259570	−	0.193745i
$628$	7.34628	−	12.7241i	0.293149	−	0.507748i
$629$	6.40359	+	11.0914i	0.255328	+	0.442241i
$630$	−22.5453	+	23.2185i	−0.898227	+	0.925046i
$631$	20.1135	−	34.8376i	0.800706	−	1.38686i	−0.118447	−	0.992960i	$-0.537791\pi$
$631$	20.1135	−	34.8376i	0.800706	−	1.38686i	0.919152	−	0.393902i	$-0.128875\pi$
$632$		−	6.87993i		−	0.273669i
$633$	−6.76489	+	6.02437i	−0.268880	+	0.239447i
$634$	4.04167	+	7.00037i	0.160515	+	0.278020i
$635$	−24.7550	+	42.8770i	−0.982374	+	1.70152i
$636$	8.03420	−	1.66178i	0.318577	−	0.0658940i
$637$	−42.9833	+	11.4697i	−1.70306	+	0.454444i
$638$			6.12098i			0.242332i
$639$	21.0110	+	15.6199i	0.831183	+	0.617913i
$640$		−	4.07740i		−	0.161173i
$641$	15.2398	−	26.3961i	0.601937	−	1.04258i	−0.390591	−	0.920564i	$-0.627729\pi$
$641$	15.2398	−	26.3961i	0.601937	−	1.04258i	0.992528	−	0.122020i	$-0.0389373\pi$
$642$	−1.82483	+	5.51332i	−0.0720203	+	0.217593i
$643$	18.1504	+	31.4373i	0.715780	+	1.23977i	0.962658	+	0.270721i	$0.0872621\pi$
$643$	18.1504	+	31.4373i	0.715780	+	1.23977i	−0.246877	+	0.969047i	$0.579405\pi$
$644$	−14.2334	−	10.9333i	−0.560873	−	0.430834i
$645$	−33.1761	+	29.5445i	−1.30631	+	1.16331i
$646$	−10.8045	−	7.55086i	−0.425098	−	0.297085i
$647$	−4.72685	+	2.72905i	−0.185832	+	0.107290i	−0.590030	−	0.807382i	$-0.700884\pi$
$647$	−4.72685	+	2.72905i	−0.185832	+	0.107290i	0.404198	+	0.914671i	$0.367551\pi$
$648$	−6.16725	+	6.55477i	−0.242272	+	0.257496i
$649$		−	8.94793i		−	0.351237i
$650$	63.9836	+	36.9410i	2.50964	+	1.44894i
$651$	−21.2231	−	10.2795i	−0.831800	−	0.402886i
$652$	7.80445	−	13.5177i	0.305646	−	0.529394i
$653$	11.0711	+	6.39190i	0.433245	+	0.250134i	0.700728	−	0.713428i	$-0.252859\pi$
$653$	11.0711	+	6.39190i	0.433245	+	0.250134i	−0.267483	+	0.963563i	$0.586192\pi$
$654$	−16.1568	−	5.34766i	−0.631780	−	0.209110i
$655$	−52.1827			−2.03895
$656$	−1.99215	−	3.45051i	−0.0777806	−	0.134720i
$657$	2.90727	−	25.0211i	0.113423	−	0.976167i
$658$	−8.33673	−	6.40385i	−0.325000	−	0.249648i
$659$	13.2530	−	22.9548i	0.516262	−	0.894192i	−0.483560	−	0.875311i	$-0.660656\pi$
$659$	13.2530	−	22.9548i	0.516262	−	0.894192i	0.999822	−	0.0188808i	$-0.00601030\pi$
$660$	5.04558	+	5.66578i	0.196399	+	0.220540i
$661$		−	27.5646i		−	1.07214i	−0.844174	−	0.536069i	$-0.819909\pi$
$661$		−	27.5646i		−	1.07214i	0.844174	−	0.536069i	$-0.180091\pi$
$662$	21.1450	+	12.2081i	0.821824	+	0.474480i
$663$	−22.1382	−	24.8594i	−0.859775	−	0.965459i
$664$			0.0397535i			0.00154274i
$665$	44.8411	−	14.1574i	1.73886	−	0.548999i
$666$	−12.6204	−	1.46640i	−0.489032	−	0.0568218i
$667$			38.6521i			1.49662i
$668$	3.87830	−	6.71742i	0.150056	−	0.259905i
$669$	9.43466	−	8.40190i	0.364765	−	0.324836i
$670$	30.9497			1.19569
$671$	−7.15337	−	4.13000i	−0.276153	−	0.159437i
$672$	−2.57291	−	3.79211i	−0.0992523	−	0.146284i
$673$		−	32.6278i		−	1.25771i	−0.777523	−	0.628854i	$-0.783524\pi$
$673$		−	32.6278i		−	1.25771i	0.777523	−	0.628854i	$-0.216476\pi$
$674$	−7.76773	+	4.48470i	−0.299202	+	0.172744i
$675$	49.4466	−	34.6982i	1.90320	−	1.33554i
$676$	13.6950	+	23.7205i	0.526732	+	0.912327i
$677$	10.8406	−	18.7764i	0.416637	−	0.721637i	−0.578961	−	0.815355i	$-0.696542\pi$
$677$	10.8406	−	18.7764i	0.416637	−	0.721637i	0.995599	+	0.0937179i	$0.0298752\pi$
$678$	−19.1948	+	3.97022i	−0.737171	+	0.152475i
$679$	−29.1683	−	22.4056i	−1.11938	−	0.859848i
$680$	6.16514	−	10.6783i	0.236422	−	0.409495i
$681$	−0.758874	−	0.852155i	−0.0290801	−	0.0326546i
$682$	−2.76404	+	4.78746i	−0.105841	+	0.183321i
$683$	−20.9807	−	36.3396i	−0.802804	−	1.39050i	−0.917764	−	0.397127i	$-0.870007\pi$
$683$	−20.9807	−	36.3396i	−0.802804	−	1.39050i	0.114960	−	0.993370i	$-0.463326\pi$
$684$	12.4064	−	4.13288i	0.474371	−	0.158024i
$685$	70.5903			2.69712
$686$	−17.0995	−	7.11395i	−0.652861	−	0.271612i
$687$	0.606063	−	1.83108i	0.0231227	−	0.0698602i
$688$	−3.14519	−	5.44764i	−0.119909	−	0.207689i
$689$	−26.0703	−	15.0517i	−0.993201	−	0.573425i
$690$	31.8613	+	35.7777i	1.21294	+	1.36203i
$691$	−0.748218	+	1.29595i	−0.0284635	+	0.0493003i	−0.879906	−	0.475147i	$-0.842395\pi$
$691$	−0.748218	+	1.29595i	−0.0284635	+	0.0493003i	0.851443	+	0.524448i	$0.175728\pi$
$692$	0.882084			0.0335318
$693$	8.26776	+	2.08550i	0.314066	+	0.0792218i
$694$	15.1730	+	8.76013i	0.575959	+	0.332530i
$695$	4.35442	+	2.51403i	0.165173	+	0.0953624i
$696$	−3.10102	+	9.36905i	−0.117544	+	0.355133i
$697$		−	12.0488i		−	0.456379i
$698$	7.55071			0.285799
$699$	−6.50446	−	31.4470i	−0.246021	−	1.18944i
$700$	11.7556	+	28.4222i	0.444322	+	1.07426i
$701$	−16.6203	+	9.59573i	−0.627740	+	0.362426i	−0.779876	−	0.625934i	$-0.784718\pi$
$701$	−16.6203	+	9.59573i	−0.627740	+	0.362426i	0.152136	+	0.988359i	$0.451385\pi$
$702$	32.8946	−	2.91179i	1.24153	−	0.109898i
$703$	15.1315	+	10.5748i	0.570693	+	0.398836i
$704$	−0.930342	+	0.537133i	−0.0350636	+	0.0202440i
$705$	18.6617	+	20.9556i	0.702840	+	0.789234i
$706$	18.3795	−	10.6114i	0.691722	−	0.399366i
$707$	21.5060	−	8.89502i	0.808815	−	0.334532i
$708$	4.53322	−	13.6961i	0.170369	−	0.514731i
$709$	11.0038	+	19.0591i	0.413255	+	0.715778i	0.995243	−	0.0974188i	$-0.0310586\pi$
$709$	11.0038	+	19.0591i	0.413255	+	0.715778i	−0.581989	+	0.813197i	$0.697725\pi$
$710$	30.8162	−	17.7917i	1.15651	−	0.667712i
$711$	8.18791	+	18.9462i	0.307071	+	0.710538i
$712$	−0.110424	−	0.191260i	−0.00413831	−	0.00716776i
$713$	−17.4541	+	30.2314i	−0.653661	+	1.13217i
$714$	−1.00445	−	13.8215i	−0.0375905	−	0.517256i
$715$		−	27.8377i		−	1.04107i
$716$	−3.25659	−	5.64058i	−0.121704	−	0.210798i
$717$	5.81905	+	28.1333i	0.217316	+	1.05066i
$718$			14.7462i			0.550322i
$719$		−	3.79925i		−	0.141688i	−0.997487	−	0.0708441i	$-0.977431\pi$
$719$		−	3.79925i		−	0.141688i	0.997487	−	0.0708441i	$-0.0225693\pi$
$720$	4.85258	+	11.2285i	0.180845	+	0.418462i
$721$	−4.55825	+	34.4855i	−0.169758	+	1.28431i
$722$	−18.7173	−	3.26550i	−0.696585	−	0.121529i
$723$	−6.73231	−	32.5486i	−0.250377	−	1.21050i
$724$	16.7223	+	9.65465i	0.621481	+	0.358812i
$725$	33.1192	−	57.3641i	1.23002	−	2.13045i
$726$	−5.35863	+	16.1899i	−0.198877	+	0.600864i
$727$	11.8028	+	20.4431i	0.437742	+	0.758191i	0.997515	−	0.0704549i	$-0.0224451\pi$
$727$	11.8028	+	20.4431i	0.437742	+	0.758191i	−0.559773	+	0.828646i	$0.689112\pi$
$728$	−2.20337	+	16.6696i	−0.0816624	+	0.617817i
$729$	9.18266	−	25.3905i	0.340098	−	0.940390i
$730$	−29.6491	−	17.1179i	−1.09736	−	0.633563i
$731$		−	19.0225i		−	0.703571i
$732$	−8.85693	−	9.94563i	−0.327362	−	0.367601i
$733$	10.2965	−	17.8340i	0.380310	−	0.658716i	−0.610797	−	0.791787i	$-0.709151\pi$
$733$	10.2965	−	17.8340i	0.380310	−	0.658716i	0.991106	+	0.133072i	$0.0424841\pi$
$734$	−24.9894			−0.922374
$735$	41.2842	+	27.1941i	1.52279	+	1.00307i
$736$	−5.87482	+	3.39183i	−0.216549	+	0.125025i
$737$	−4.07714	−	7.06182i	−0.150183	−	0.260125i
$738$	9.59258	+	7.13126i	0.353108	+	0.262505i
$739$	14.2365	−	24.6583i	0.523698	−	0.907072i	−0.475921	−	0.879488i	$-0.657885\pi$
$739$	14.2365	−	24.6583i	0.523698	−	0.907072i	0.999619	−	0.0275839i	$-0.00878135\pi$
$740$	−8.63413	+	14.9547i	−0.317397	+	0.549747i
$741$	−44.0811	−	18.9497i	−1.61936	−	0.696135i
$742$	−4.78988	−	11.5807i	−0.175842	−	0.425142i
$743$	−22.0790	−	38.2419i	−0.809998	−	1.40296i	−0.912864	−	0.408263i	$-0.866135\pi$
$743$	−22.0790	−	38.2419i	−0.809998	−	1.40296i	0.102866	−	0.994695i	$-0.467199\pi$
$744$	−6.65621	+	5.92759i	−0.244028	+	0.217316i
$745$	72.8571			2.66928
$746$	4.75225	+	2.74372i	0.173992	+	0.100455i
$747$	−0.0473113	−	0.109475i	−0.00173103	−	0.00400547i
$748$	−3.24864			−0.118782
$749$	8.79457	+	1.16246i	0.321346	+	0.0424752i
$750$	−9.47717	−	45.8192i	−0.346057	−	1.67308i
$751$	−20.3837	+	11.7685i	−0.743811	+	0.429440i	−0.823453	−	0.567384i	$-0.807956\pi$
$751$	−20.3837	+	11.7685i	−0.743811	+	0.429440i	0.0796421	+	0.996824i	$0.474622\pi$
$752$	−3.44099	+	1.98666i	−0.125480	+	0.0724459i
$753$	−4.77601	−	1.58079i	−0.174047	−	0.0576072i
$754$	31.3600	−	18.1057i	1.14207	−	0.659372i
$755$	−41.6156	−	72.0804i	−1.51455	−	2.62327i
$756$	11.5984	+	7.38080i	0.421831	+	0.268437i
$757$	−16.0174	−	27.7430i	−0.582163	−	1.00834i	−0.995223	−	0.0976315i	$-0.968873\pi$
$757$	−16.0174	−	27.7430i	−0.582163	−	1.00834i	0.413060	−	0.910704i	$-0.364460\pi$
$758$		−	20.9015i		−	0.759178i
$759$	3.96618	−	11.9829i	0.143963	−	0.434953i
$760$	1.53302	−	17.7067i	0.0556085	−	0.642291i
$761$	−26.4000	−	15.2420i	−0.956999	−	0.552524i	−0.0617510	−	0.998092i	$-0.519668\pi$
$761$	−26.4000	−	15.2420i	−0.956999	−	0.552524i	−0.895248	+	0.445568i	$0.853002\pi$
$762$	19.9663	+	6.60855i	0.723302	+	0.239403i
$763$	−3.40658	+	25.7725i	−0.123326	+	0.933025i
$764$	7.77719	+	4.49016i	0.281369	+	0.162448i
$765$	−4.26933	+	36.7436i	−0.154358	+	1.32847i
$766$	−19.1265			−0.691068
$767$	−45.8435	+	26.4678i	−1.65531	+	0.955696i
$768$	−1.69615	+	0.350829i	−0.0612045	+	0.0126595i
$769$	24.0254	−	41.6132i	0.866377	−	1.50061i	0.000704420	−	1.00000i	$-0.499776\pi$
$769$	24.0254	−	41.6132i	0.866377	−	1.50061i	0.865673	−	0.500610i	$-0.166891\pi$
$770$	7.05967	−	9.19049i	0.254413	−	0.331202i
$771$	24.5651	+	27.5846i	0.884690	+	0.993436i
$772$	0.0705418	+	0.0407273i	0.00253886	+	0.00146581i
$773$	32.6930			1.17589			0.587943	−	0.808903i	$-0.299938\pi$
$773$	32.6930			1.17589			0.587943	+	0.808903i	$0.299938\pi$
$774$	15.1447	+	11.2588i	0.544364	+	0.404688i
$775$	51.8077	−	29.9112i	1.86099	−	1.07444i
$776$	−12.0392	+	6.95084i	−0.432183	+	0.249521i
$777$	1.40670	+	19.3567i	0.0504652	+	0.694417i
$778$			30.6695i			1.09955i
$779$	−7.35391	−	15.7334i	−0.263481	−	0.563707i
$780$	14.1032	−	42.6096i	0.504975	−	1.52567i
$781$	−8.11909	−	4.68756i	−0.290524	−	0.167734i
$782$	−20.5141			−0.733584
$783$	−2.61055	−	29.4914i	−0.0932933	−	1.05394i
$784$	−4.95487	+	4.94462i	−0.176960	+	0.176594i
$785$	51.8814	+	29.9538i	1.85173	+	1.06910i
$786$	4.48992	+	21.7074i	0.160150	+	0.774276i
$787$	−11.3817	+	6.57120i	−0.405712	+	0.234238i	−0.688946	−	0.724813i	$-0.741926\pi$
$787$	−11.3817	+	6.57120i	−0.405712	+	0.234238i	0.283234	+	0.959051i	$0.408593\pi$
$788$			22.2690i			0.793301i
$789$	−47.2438	−	15.6370i	−1.68192	−	0.556693i
$790$	28.0522			0.998054
$791$	11.4437	+	27.6679i	0.406890	+	0.983758i
$792$	1.92276	−	2.58639i	0.0683223	−	0.0919035i
$793$			48.8658i			1.73528i
$794$	−13.3341			−0.473211
$795$	6.77576	+	32.7587i	0.240311	+	1.16183i
$796$	3.50713			0.124307
$797$	25.4281			0.900709			0.450354	−	0.892850i	$-0.351298\pi$
$797$	25.4281			0.900709			0.450354	+	0.892850i	$0.351298\pi$
$798$	−9.74752	−	17.4352i	−0.345058	−	0.617199i
$799$	−12.0155			−0.425078
$800$	11.6252			0.411013
$801$	0.531711	+	0.395281i	0.0187871	+	0.0139666i
$802$	2.19502			0.0775088
$803$			9.02006i			0.318311i
$804$	−2.66299	−	12.8747i	−0.0939163	−	0.454056i
$805$	44.5797	−	58.0351i	1.57123	−	2.04547i
$806$	32.7039			1.15195
$807$	3.44221	−	10.3999i	0.121172	−	0.366093i
$808$		−	8.79633i		−	0.309454i
$809$	−9.16404	+	5.29086i	−0.322191	+	0.186017i	−0.652369	−	0.757902i	$-0.726225\pi$
$809$	−9.16404	+	5.29086i	−0.322191	+	0.186017i	0.330178	+	0.943919i	$0.392891\pi$
$810$	−26.7265	−	25.1463i	−0.939072	−	0.883553i
$811$	−12.0831	−	6.97618i	−0.424295	−	0.244967i	0.272618	−	0.962122i	$-0.412110\pi$
$811$	−12.0831	−	6.97618i	−0.424295	−	0.244967i	−0.696913	+	0.717156i	$0.745444\pi$
$812$	14.9450	+	1.97542i	0.524468	+	0.0693236i
$813$	19.0513	−	3.94054i	0.668158	−	0.138201i
$814$	4.54964			0.159465
$815$	55.1171	+	31.8219i	1.93067	+	1.11467i
$816$	−4.97251	−	1.64583i	−0.174073	−	0.0576156i
$817$	−11.6103	−	24.8397i	−0.406193	−	0.869032i
$818$		−	3.79885i		−	0.132824i
$819$	−13.7710	−	48.5277i	−0.481199	−	1.69569i
$820$	14.0691	−	8.12282i	0.491315	−	0.283661i
$821$	−9.80498	+	5.66091i	−0.342196	+	0.197567i	−0.661243	−	0.750172i	$-0.729971\pi$
$821$	−9.80498	+	5.66091i	−0.342196	+	0.197567i	0.319047	+	0.947739i	$0.396637\pi$
$822$	−6.07375	−	29.3647i	−0.211846	−	1.02421i
$823$	22.1713			0.772843			0.386422	−	0.922322i	$-0.373711\pi$
$823$	22.1713			0.772843			0.386422	+	0.922322i	$0.373711\pi$
$824$	11.3862	+	6.57382i	0.396657	+	0.229010i
$825$	−16.1539	+	14.3856i	−0.562406	+	0.500843i
$826$	−21.8473	−	2.88776i	−0.760165	−	0.100478i
$827$	−20.8618	+	36.1336i	−0.725434	+	1.25649i	0.233361	+	0.972390i	$0.425028\pi$
$827$	−20.8618	+	36.1336i	−0.725434	+	1.25649i	−0.958795	+	0.284099i	$0.908306\pi$
$828$	12.1416	−	16.3323i	0.421951	−	0.567586i
$829$	30.2594	−	17.4703i	1.05095	−	0.606769i	0.128038	−	0.991769i	$-0.459132\pi$
$829$	30.2594	−	17.4703i	1.05095	−	0.606769i	0.922916	+	0.385001i	$0.125799\pi$
$830$	−0.162091			−0.00562626
$831$	−15.9895	−	17.9549i	−0.554669	−	0.622849i
$832$	5.50387	+	3.17766i	0.190812	+	0.110166i
$833$	−20.4527	+	5.45761i	−0.708645	+	0.189095i
$834$	0.671139	−	2.02770i	0.0232396	−	0.0702134i
$835$	27.3896	+	15.8134i	0.947857	+	0.547245i
$836$	−4.24211	+	1.98279i	−0.146716	+	0.0685764i
$837$	11.2756	−	24.2453i	0.389742	−	0.838039i
$838$			16.5211i			0.570711i
$839$	−2.18245	−	3.78011i	−0.0753465	−	0.130504i	0.825890	−	0.563831i	$-0.190673\pi$
$839$	−2.18245	−	3.78011i	−0.0753465	−	0.130504i	−0.901237	+	0.433327i	$0.857340\pi$
$840$	15.4620	−	10.4908i	0.533489	−	0.361967i
$841$	−1.73258	−	3.00092i	−0.0597442	−	0.103480i
$842$	−7.50592	+	4.33355i	−0.258671	+	0.149344i
$843$	−5.40526	+	16.3308i	−0.186167	+	0.562462i
$844$	4.52926	−	2.61497i	0.155904	−	0.0900110i
$845$	−96.7180	+	55.8402i	−3.32720	+	1.92096i
$846$	7.11157	−	9.56610i	0.244501	−	0.328889i
$847$	25.8253	+	3.41356i	0.887368	+	0.117291i
$848$	−4.73673			−0.162660
$849$	−2.65940	+	8.03479i	−0.0912704	+	0.275753i
$850$	30.4453	+	17.5776i	1.04427	+	0.602907i
$851$	28.7296			0.984837
$852$	−10.0526	−	11.2883i	−0.344398	−	0.386731i
$853$	−13.8221	−	23.9406i	−0.473260	−	0.819710i	0.526272	−	0.850316i	$-0.323589\pi$
$853$	−13.8221	−	23.9406i	−0.473260	−	0.819710i	−0.999532	+	0.0306066i	$0.990256\pi$
$854$	−12.3924	+	16.1329i	−0.424061	+	0.552055i
$855$	16.8514	+	50.5860i	0.576306	+	1.73000i
$856$	1.67647	−	2.90374i	0.0573007	−	0.0992476i
$857$	6.56082	−	11.3637i	0.224113	−	0.388176i	−0.731940	−	0.681369i	$-0.761385\pi$
$857$	6.56082	−	11.3637i	0.224113	−	0.388176i	0.956053	+	0.293194i	$0.0947180\pi$
$858$	−11.5801	+	2.39522i	−0.395339	+	0.0817714i
$859$	19.0279	+	32.9574i	0.649225	+	1.12449i	0.983308	+	0.181947i	$0.0582399\pi$
$859$	19.0279	+	32.9574i	0.649225	+	1.12449i	−0.334083	+	0.942544i	$0.608427\pi$
$860$	22.2122	−	12.8242i	0.757430	−	0.437302i
$861$	7.95909	−	16.4323i	0.271245	−	0.560013i
$862$	4.88374			0.166341
$863$	22.1882	−	38.4312i	0.755297	−	1.30821i	−0.189930	−	0.981798i	$-0.560826\pi$
$863$	22.1882	−	38.4312i	0.755297	−	1.30821i	0.945227	−	0.326415i	$-0.105841\pi$
$864$	4.25339	−	2.98474i	0.144703	−	0.101543i
$865$			3.59661i			0.122288i
$866$	−9.13958	−	5.27674i	−0.310576	−	0.179311i
$867$	9.04832	+	10.1605i	0.307297	+	0.345070i
$868$	10.7971	+	8.29376i	0.366476	+	0.281509i
$869$	−3.69544	−	6.40069i	−0.125359	−	0.217129i
$870$	−38.2014	−	12.6441i	−1.29515	−	0.428676i
$871$	−24.1202	+	41.7774i	−0.817282	+	1.41557i
$872$	8.50939	+	4.91290i	0.288164	+	0.166372i
$873$	24.8817	−	33.4696i	0.842119	−	1.13277i
$874$	−26.7876	+	12.5207i	−0.906104	+	0.423520i
$875$	−66.0451	+	27.3167i	−2.23273	+	0.923475i
$876$	−4.56976	+	13.8065i	−0.154398	+	0.466479i
$877$		−	9.22011i		−	0.311341i	−0.987809	−	0.155671i	$-0.950246\pi$
$877$		−	9.22011i		−	0.311341i	0.987809	−	0.155671i	$-0.0497538\pi$
$878$			9.52603i			0.321488i
$879$	8.86006	−	1.83260i	0.298843	−	0.0618122i
$880$	−2.19011	−	3.79338i	−0.0738286	−	0.127875i
$881$		−	7.14044i		−	0.240568i	−0.992740	−	0.120284i	$-0.961620\pi$
$881$		−	7.14044i		−	0.240568i	0.992740	−	0.120284i	$-0.0383804\pi$
$882$	7.76023	−	19.5136i	0.261300	−	0.657056i
$883$	−21.5312	+	37.2932i	−0.724583	+	1.25501i	0.234562	+	0.972101i	$0.424634\pi$
$883$	−21.5312	+	37.2932i	−0.724583	+	1.25501i	−0.959145	+	0.282914i	$0.908699\pi$
$884$	9.60940	+	16.6440i	0.323199	+	0.559797i
$885$	55.8445	+	18.4837i	1.87719	+	0.621324i
$886$	25.2198	−	14.5607i	0.847276	−	0.489175i
$887$	6.56550	+	11.3718i	0.220448	+	0.381827i	0.954944	−	0.296786i	$-0.0959147\pi$
$887$	6.56550	+	11.3718i	0.220448	+	0.381827i	−0.734496	+	0.678613i	$0.762581\pi$
$888$	6.96389	+	2.30495i	0.233693	+	0.0773490i
$889$	4.20979	−	31.8492i	0.141192	−	1.06819i
$890$	0.779843	−	0.450242i	0.0261404	−	0.0150922i
$891$	−2.21686	+	9.41082i	−0.0742677	+	0.315274i
$892$	−6.31674	+	3.64697i	−0.211500	+	0.122110i
$893$	−15.6900	+	7.33362i	−0.525045	+	0.245410i
$894$	−6.26880	−	30.3077i	−0.209660	−	1.01364i
$895$	22.9989	−	13.2784i	0.768769	−	0.443849i
$896$	1.01122	+	2.44488i	0.0337825	+	0.0816777i
$897$	−73.1249	+	15.1251i	−2.44157	+	0.505011i
$898$	−37.7884			−1.26102
$899$		−	29.3205i		−	0.977894i
$900$	−32.0139	+	13.8354i	−1.06713	+	0.461178i
$901$	−12.4050	−	7.16206i	−0.413272	−	0.238603i
$902$	−3.70677	−	2.14011i	−0.123422	−	0.0712577i
$903$	12.5657	−	25.9432i	0.418162	−	0.863337i
$904$	11.3167			0.376387
$905$	−39.3659	+	68.1837i	−1.30857	+	2.26650i
$906$	−26.4038	+	23.5135i	−0.877209	+	0.781185i
$907$	22.6413	+	13.0719i	0.751791	+	0.434047i	0.826341	−	0.563170i	$-0.190419\pi$
$907$	22.6413	+	13.0719i	0.751791	+	0.434047i	−0.0745496	+	0.997217i	$0.523752\pi$
$908$	0.329401	+	0.570539i	0.0109315	+	0.0189340i
$909$	10.4687	+	24.2237i	0.347223	+	0.803448i
$910$	−67.9687	−	8.98403i	−2.25314	−	0.297818i
$911$	32.7316			1.08445			0.542224	−	0.840234i	$-0.317583\pi$
$911$	32.7316			1.08445			0.542224	+	0.840234i	$0.317583\pi$
$912$	−7.49769	+	0.885812i	−0.248273	+	0.0293322i
$913$	0.0213529	+	0.0369844i	0.000706679	+	0.00122400i
$914$	2.19166	−	3.79607i	0.0724937	−	0.125563i
$915$	40.5523	−	36.1133i	1.34062	−	1.19387i
$916$	−0.556790	+	0.964389i	−0.0183969	+	0.0318643i
$917$	31.2896	−	12.9416i	1.03327	−	0.427370i
$918$	15.6522	−	1.38552i	0.516600	−	0.0457288i
$919$	−19.0561	+	33.0061i	−0.628603	+	1.08877i	0.359230	+	0.933249i	$0.383039\pi$
$919$	−19.0561	+	33.0061i	−0.628603	+	1.08877i	−0.987832	+	0.155522i	$0.950294\pi$
$920$	−13.8299	−	23.9540i	−0.455957	−	0.789741i
$921$	8.07733	−	7.19315i	0.266157	−	0.237022i
$922$	11.0809	−	6.39758i	0.364931	−	0.210693i
$923$			55.4628i			1.82558i
$924$	−4.43056	−	2.14596i	−0.145755	−	0.0705971i
$925$	−42.6379	−	24.6170i	−1.40193	−	0.809403i
$926$	−1.81932			−0.0597866
$927$	−39.1794	−	4.55235i	−1.28682	−	0.149519i
$928$	2.84891	−	4.93446i	0.0935201	−	0.161982i
$929$		−	36.0008i		−	1.18115i	−0.806983	−	0.590574i	$-0.798901\pi$
$929$		−	36.0008i		−	1.18115i	0.806983	−	0.590574i	$-0.201099\pi$
$930$	−24.1692	−	27.1400i	−0.792538	−	0.889957i
$931$	−23.3764	+	19.6098i	−0.766129	+	0.642687i
$932$			18.5403i			0.607307i
$933$	−20.0349	+	17.8418i	−0.655914	+	0.584114i
$934$	15.3869	+	8.88363i	0.503475	+	0.290681i
$935$		−	13.2460i		−	0.433191i
$936$	−18.9385	−	2.20052i	−0.619026	−	0.0719261i
$937$	−24.8204	+	42.9901i	−0.810846	+	1.40443i	0.101427	+	0.994843i	$0.467659\pi$
$937$	−24.8204	+	42.9901i	−0.810846	+	1.40443i	−0.912273	+	0.409583i	$0.865674\pi$
$938$	−18.5580	+	7.67572i	−0.605940	+	0.250621i
$939$	−6.04995	−	6.79361i	−0.197433	−	0.221701i
$940$	−8.10039	−	14.0303i	−0.264206	−	0.457618i
$941$	3.92865			0.128070			0.0640351	−	0.997948i	$-0.479603\pi$
$941$	3.92865			0.128070			0.0640351	+	0.997948i	$0.479603\pi$
$942$	7.99639	−	24.1593i	0.260536	−	0.787153i
$943$	−23.4071	−	13.5141i	−0.762241	−	0.440080i
$944$	−4.16467	+	7.21341i	−0.135548	+	0.234777i
$945$	−30.0945	+	47.2915i	−0.978973	+	1.53839i
$946$	−5.85222	−	3.37878i	−0.190272	−	0.109854i
$947$			3.69623i			0.120111i	0.998195	+	0.0600556i	$0.0191278\pi$
$947$			3.69623i			0.120111i	−0.998195	+	0.0600556i	$0.980872\pi$
$948$	−2.41368	−	11.6694i	−0.0783926	−	0.379004i
$949$	46.2131	−	26.6812i	1.50014	−	0.866107i
$950$	50.4843	+	4.37084i	1.63793	+	0.141809i
$951$	9.31120	+	10.4557i	0.301936	+	0.339051i
$952$	−1.04843	+	7.93190i	−0.0339798	+	0.257074i
$953$	8.58734	+	14.8737i	0.278171	+	0.481806i	0.970930	−	0.239363i	$-0.0769385\pi$
$953$	8.58734	+	14.8737i	0.278171	+	0.481806i	−0.692759	+	0.721169i	$0.743605\pi$
$954$	13.0442	−	5.63726i	0.422321	−	0.182513i
$955$	−18.3082	+	31.7107i	−0.592439	+	1.02613i
$956$		−	16.5866i		−	0.536448i
$957$	2.14742	+	10.3821i	0.0694162	+	0.335605i
$958$		−	14.5072i		−	0.468705i
$959$	−42.3271	+	17.5068i	−1.36681	+	0.565325i
$960$	−1.43047	−	6.91588i	−0.0461683	−	0.223209i
$961$	−2.25977	+	3.91404i	−0.0728958	+	0.126259i
$962$	−13.4577	−	23.3095i	−0.433895	−	0.751528i
$963$	−1.16095	+	9.99161i	−0.0374111	+	0.321975i
$964$			19.1897i			0.618059i
$965$	−0.166062	+	0.287627i	−0.00534572	+	0.00925905i
$966$	−27.9776	−	13.5511i	−0.900165	−	0.436000i
$967$	9.14064	+	15.8321i	0.293943	+	0.509125i	0.974739	−	0.223349i	$-0.0716990\pi$
$967$	9.14064	+	15.8321i	0.293943	+	0.509125i	−0.680795	+	0.732474i	$0.738366\pi$
$968$	4.92298	−	8.52684i	0.158230	−	0.274063i
$969$	−20.9751	−	9.01684i	−0.673817	−	0.289663i
$970$	−28.3414	−	49.0887i	−0.909987	−	1.57614i
$971$	−6.83298			−0.219281			−0.109640	−	0.993971i	$-0.534970\pi$
$971$	−6.83298			−0.219281			−0.109640	+	0.993971i	$0.534970\pi$
$972$	−8.16096	+	13.2815i	−0.261763	+	0.426005i
$973$	−3.23448	−	0.427530i	−0.103693	−	0.0137060i
$974$	−2.57977	+	1.48943i	−0.0826611	+	0.0477244i
$975$	121.486	+	40.2100i	3.89065	+	1.28775i
$976$	3.84448	+	6.65884i	0.123059	+	0.213144i
$977$	−10.4175	−	18.0437i	−0.333286	−	0.577268i	0.649868	−	0.760047i	$-0.274824\pi$
$977$	−10.4175	−	18.0437i	−0.333286	−	0.577268i	−0.983154	+	0.182779i	$0.941491\pi$
$978$	8.49510	−	25.6661i	0.271643	−	0.820710i
$979$	−0.205464	−	0.118625i	−0.00656666	−	0.00379126i
$980$	−20.1612	−	20.2030i	−0.644026	−	0.645361i
$981$	−29.2804	−	3.40216i	−0.934851	−	0.108623i
$982$	−21.7386	+	12.5508i	−0.693706	+	0.400511i
$983$	9.33445	−	16.1677i	0.297723	−	0.515671i	−0.677892	−	0.735162i	$-0.737106\pi$
$983$	9.33445	−	16.1677i	0.297723	−	0.515671i	0.975615	+	0.219491i	$0.0704396\pi$
$984$	−4.58953	−	5.15368i	−0.146309	−	0.164293i
$985$	−90.7998			−2.89312
$986$	14.9221	−	8.61525i	0.475215	−	0.274365i
$987$	−16.3870	−	7.93712i	−0.521604	−	0.252641i
$988$	22.7067	+	15.8688i	0.722395	+	0.504854i
$989$	−36.9549	−	21.3359i	−1.17510	−	0.678444i
$990$	10.5458	+	7.83987i	0.335167	+	0.249167i
$991$	35.6196	+	20.5650i	1.13149	+	0.653269i	0.944310	−	0.329056i	$-0.106731\pi$
$991$	35.6196	+	20.5650i	1.13149	+	0.653269i	0.187184	+	0.982325i	$0.440064\pi$
$992$	4.45649	−	2.57296i	0.141494	−	0.0816915i
$993$	40.1480	+	13.2884i	1.27406	+	0.421695i
$994$	−14.0654	+	18.3108i	−0.446129	+	0.580784i
$995$			14.3000i			0.453340i
$996$	0.0139467	+	0.0674279i	0.000441918	+	0.00213653i
$997$	−37.6834			−1.19344			−0.596722	−	0.802448i	$-0.703531\pi$
$997$	−37.6834			−1.19344			−0.596722	+	0.802448i	$0.703531\pi$
$998$	20.7249			0.656035
$999$	−21.9206	+	1.94038i	−0.693536	+	0.0613910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.p.c.107.3	✓	50
3.2	odd	2		798.2.p.d.107.11	yes	50
7.4	even	3		798.2.bh.d.221.19	yes	50
19.8	odd	6		798.2.bh.c.65.7	yes	50
21.11	odd	6		798.2.bh.c.221.7	yes	50
57.8	even	6		798.2.bh.d.65.19	yes	50
133.46	odd	6		798.2.p.d.179.11	yes	50
399.179	even	6	inner	798.2.p.c.179.3	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.p.c.107.3	✓	50	1.1	even	1	trivial
798.2.p.c.179.3	yes	50	399.179	even	6	inner
798.2.p.d.107.11	yes	50	3.2	odd	2
798.2.p.d.179.11	yes	50	133.46	odd	6
798.2.bh.c.65.7	yes	50	19.8	odd	6
798.2.bh.c.221.7	yes	50	21.11	odd	6
798.2.bh.d.65.19	yes	50	57.8	even	6
798.2.bh.d.221.19	yes	50	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.69615 + 0.350829i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(1.69615 - 0.350829i) q^{6} +(-1.01122 - 2.44488i) q^{7} -1.00000 q^{8} +(2.75384 - 1.19012i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.69615 + 0.350829i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(1.69615 - 0.350829i) q^{6} +(-1.01122 - 2.44488i) q^{7} -1.00000 q^{8} +(2.75384 - 1.19012i) q^{9} -4.07740i q^{10} +(-0.930342 + 0.537133i) q^{11} +(-1.69615 + 0.350829i) q^{12} +(5.50387 + 3.17766i) q^{13} +(1.01122 + 2.44488i) q^{14} +(-1.43047 - 6.91588i) q^{15} +1.00000 q^{16} +(2.61890 + 1.51203i) q^{17} +(-2.75384 + 1.19012i) q^{18} +(4.34265 + 0.375980i) q^{19} +4.07740i q^{20} +(2.57291 + 3.79211i) q^{21} +(0.930342 - 0.537133i) q^{22} +(5.87482 - 3.39183i) q^{23} +(1.69615 - 0.350829i) q^{24} -11.6252 q^{25} +(-5.50387 - 3.17766i) q^{26} +(-4.25339 + 2.98474i) q^{27} +(-1.01122 - 2.44488i) q^{28} +(-2.84891 + 4.93446i) q^{29} +(1.43047 + 6.91588i) q^{30} +(-4.45649 + 2.57296i) q^{31} -1.00000 q^{32} +(1.38956 - 1.23745i) q^{33} +(-2.61890 - 1.51203i) q^{34} +(9.96876 - 4.12315i) q^{35} +(2.75384 - 1.19012i) q^{36} +(3.66771 + 2.11756i) q^{37} +(-4.34265 - 0.375980i) q^{38} +(-10.4502 - 3.45886i) q^{39} -4.07740i q^{40} +(-1.99215 - 3.45051i) q^{41} +(-2.57291 - 3.79211i) q^{42} +(-3.14519 - 5.44764i) q^{43} +(-0.930342 + 0.537133i) q^{44} +(4.85258 + 11.2285i) q^{45} +(-5.87482 + 3.39183i) q^{46} +(-3.44099 + 1.98666i) q^{47} +(-1.69615 + 0.350829i) q^{48} +(-4.95487 + 4.94462i) q^{49} +11.6252 q^{50} +(-4.97251 - 1.64583i) q^{51} +(5.50387 + 3.17766i) q^{52} -4.73673 q^{53} +(4.25339 - 2.98474i) q^{54} +(-2.19011 - 3.79338i) q^{55} +(1.01122 + 2.44488i) q^{56} +(-7.49769 + 0.885812i) q^{57} +(2.84891 - 4.93446i) q^{58} +(-4.16467 + 7.21341i) q^{59} +(-1.43047 - 6.91588i) q^{60} +(3.84448 + 6.65884i) q^{61} +(4.45649 - 2.57296i) q^{62} +(-5.69443 - 5.52933i) q^{63} +1.00000 q^{64} +(-12.9566 + 22.4415i) q^{65} +(-1.38956 + 1.23745i) q^{66} +7.59056i q^{67} +(2.61890 + 1.51203i) q^{68} +(-8.77462 + 7.81411i) q^{69} +(-9.96876 + 4.12315i) q^{70} +(4.36350 + 7.55780i) q^{71} +(-2.75384 + 1.19012i) q^{72} +(4.19824 - 7.27157i) q^{73} +(-3.66771 - 2.11756i) q^{74} +(19.7181 - 4.07846i) q^{75} +(4.34265 + 0.375980i) q^{76} +(2.25401 + 1.73141i) q^{77} +(10.4502 + 3.45886i) q^{78} +6.87993i q^{79} +4.07740i q^{80} +(6.16725 - 6.55477i) q^{81} +(1.99215 + 3.45051i) q^{82} -0.0397535i q^{83} +(2.57291 + 3.79211i) q^{84} +(-6.16514 + 10.6783i) q^{85} +(3.14519 + 5.44764i) q^{86} +(3.10102 - 9.36905i) q^{87} +(0.930342 - 0.537133i) q^{88} +(0.110424 + 0.191260i) q^{89} +(-4.85258 - 11.2285i) q^{90} +(2.20337 - 16.6696i) q^{91} +(5.87482 - 3.39183i) q^{92} +(6.65621 - 5.92759i) q^{93} +(3.44099 - 1.98666i) q^{94} +(-1.53302 + 17.7067i) q^{95} +(1.69615 - 0.350829i) q^{96} +(12.0392 - 6.95084i) q^{97} +(4.95487 - 4.94462i) q^{98} +(-1.92276 + 2.58639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 50 q^{2} - 3 q^{3} + 50 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9}+O(q^{10}) \) 50 * q - 50 * q^2 - 3 * q^3 + 50 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9	\( 50 q - 50 q^{2} - 3 q^{3} + 50 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 17 q^{15} + 50 q^{16} - 3 q^{17} + 3 q^{18} + 10 q^{19} + 4 q^{21} - 3 q^{22} - 9 q^{23} + 3 q^{24} - 58 q^{25} + 3 q^{26} - 6 q^{27} + 5 q^{29} + 17 q^{30} + 15 q^{31} - 50 q^{32} + q^{33} + 3 q^{34} - 3 q^{36} - 9 q^{37} - 10 q^{38} - 17 q^{39} + 17 q^{41} - 4 q^{42} + 15 q^{43} + 3 q^{44} + 26 q^{45} + 9 q^{46} - 21 q^{47} - 3 q^{48} + 8 q^{49} + 58 q^{50} - 23 q^{51} - 3 q^{52} + 12 q^{53} + 6 q^{54} - 16 q^{55} - 4 q^{57} - 5 q^{58} + q^{59} - 17 q^{60} + 23 q^{61} - 15 q^{62} - 16 q^{63} + 50 q^{64} + 14 q^{65} - q^{66} - 3 q^{68} + 31 q^{69} - 3 q^{71} + 3 q^{72} + 15 q^{73} + 9 q^{74} + 8 q^{75} + 10 q^{76} + 57 q^{77} + 17 q^{78} + 77 q^{81} - 17 q^{82} + 4 q^{84} - 10 q^{85} - 15 q^{86} + 19 q^{87} - 3 q^{88} - 33 q^{89} - 26 q^{90} - 15 q^{91} - 9 q^{92} + 53 q^{93} + 21 q^{94} - 30 q^{95} + 3 q^{96} - 21 q^{97} - 8 q^{98} + 19 q^{99}+O(q^{100}) \) 50 * q - 50 * q^2 - 3 * q^3 + 50 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 17 * q^15 + 50 * q^16 - 3 * q^17 + 3 * q^18 + 10 * q^19 + 4 * q^21 - 3 * q^22 - 9 * q^23 + 3 * q^24 - 58 * q^25 + 3 * q^26 - 6 * q^27 + 5 * q^29 + 17 * q^30 + 15 * q^31 - 50 * q^32 + q^33 + 3 * q^34 - 3 * q^36 - 9 * q^37 - 10 * q^38 - 17 * q^39 + 17 * q^41 - 4 * q^42 + 15 * q^43 + 3 * q^44 + 26 * q^45 + 9 * q^46 - 21 * q^47 - 3 * q^48 + 8 * q^49 + 58 * q^50 - 23 * q^51 - 3 * q^52 + 12 * q^53 + 6 * q^54 - 16 * q^55 - 4 * q^57 - 5 * q^58 + q^59 - 17 * q^60 + 23 * q^61 - 15 * q^62 - 16 * q^63 + 50 * q^64 + 14 * q^65 - q^66 - 3 * q^68 + 31 * q^69 - 3 * q^71 + 3 * q^72 + 15 * q^73 + 9 * q^74 + 8 * q^75 + 10 * q^76 + 57 * q^77 + 17 * q^78 + 77 * q^81 - 17 * q^82 + 4 * q^84 - 10 * q^85 - 15 * q^86 + 19 * q^87 - 3 * q^88 - 33 * q^89 - 26 * q^90 - 15 * q^91 - 9 * q^92 + 53 * q^93 + 21 * q^94 - 30 * q^95 + 3 * q^96 - 21 * q^97 - 8 * q^98 + 19 * q^99

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